Kamchatka State Technical University
A. Isakov
Solving Unified State Examination problems - 2014
Petropavlovsk-Kamchatsky
UDC 50(075.8)
Reviewer Doctor of Physical and Mathematical Sciences,
Professor of the Far Eastern Federal University Stotsenko L.G.
Isakov Alexander Yakovlevich
I85 Physics. Solving Unified State Examination problems - 2014. Part 1: KamchatSTU, 2013. - 172 p.
Solutions to problems from a collection of variant tasks by A.G. Gribov, planned, in the author’s opinion, for inclusion in examination materials in physics in 2014 are presented.
Most problems are provided with detailed solutions with an analysis of the applicable laws and definitions; for standard problems of the most basic level, only solution diagrams are provided
The collection is intended, first of all, for high school students who intend to master methods for solving problems, in particular, part “C” within the framework of the modern Unified State Exam.
The materials presented can also be useful to first-year students studying general physics at a university level in technical training programs, especially to students of correspondence education, when the program is mastered independently.
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Option 1
A1. Four bodies moved along the Ox axis. The table shows the dependence of their coordinates on time:
Which body could have a constant speed that was different from zero?
1. It is possible to visualize the meaning of the decision using motion graphs, i.e. dependencies of body coordinates on time:
from which it is clear that only in the first case the value of the average speed of movement in projection onto a given axis remains constant throughout the movement
< v x1 >= |
Const; |
|
2. The speed of the second body remains equal to zero during the entire movement, which does not satisfy the condition set in the problem
v x 2 = 0;
3. The third body is moving accelerated, so
v x3 = kt 2,
where k is some constant coefficient, i.e. The modulus of the velocity projection onto the Ox axis depends on time.
4. The fourth body at t2 = 2 s and t4 = 4 s stops (vx 4 = 0) and changes the direction of movement.
A2. The ball moves in a circle of radius r with speed v. How will its normal (centripetal acceleration) change if the radius of the circle is increased by 3 times, leaving the modulus of the ball’s velocity the same?
1. Any body moving along a curved path (which includes a circle) always has an acceleration different from zero, because:
a r = ddt v ,
It should be noted that the time derivative is taken from the velocity vector, which, like any vector, is characterized by modulus (magnitude) and direction. During curvilinear motion, even with a constant velocity modulus, the direction changes - therefore, such motion, by definition, is accelerated.
2. When considering curvilinear motion from a kinematic point of view, it is customary to represent acceleration in the form of two components - tangential (tangential) aτ and normal (centripetal) acceleration ar n:
ar = ar τ + ar n ; |
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ar τ |
ar n |
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3. Thus, based on the written equations, it is clear that the tangential acceleration vector remains constant in magnitude and directed tangentially at a given point of the trajectory. A mole of normal acceleration, inversely proportional to the radius of the circle, will decrease by a factor of three as that radius increases by a factor of three.
A3. Near the surface of the Moon, a gravitational force F1 = 120 N acts on an astronaut. What gravitational force acts from the Moon on the same astronaut in a spacecraft moving in a circular orbit around the Moon at a distance of three lunar radii from its center?
1. There is a gravitational interaction between the astronaut and the Moon in accordance with Newton’s law:
F=G |
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F=G |
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(3R) |
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where G is the gravitational constant established by Cavendish, M and m are the mass of the Moon and the astronaut, R is the radius of the Moon.
2. Dividing the equations by each other we get:
9R 2 |
; F= |
≈ 13.3 H; |
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A4. The balls move at the speeds shown in the figure and collide. How will the total momentum of the balls be directed after the collision if the impact is absolutely elastic?
1. In an absolutely elastic collision of bodies, both momentum and kinetic energy are conserved; the sum of the momentum of the bodies before the collision is equal to the sum of the momentum of the bodies after the collision, which allows us to write the following equation for the final momentum of the bodies:
1.2 = p r |
1 + p r |
P1 2 + p2 2 + 2p1 p2 cos(pr |
1 ;pr |
2); cos(pr |
1 ;pr |
2 ) = 0; |
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p r 1.2 = p 12 + p 2 2 ;
A5. The boy pushed the sled off the top of the slide. Immediately after the point, the sled had a speed of v1 = 5 m/s, and at the foot of the slide it was equal to v2 = 15 m/s. The friction of the sled on the snow is negligible. What is the height of the slide?
1. The movement of the sled down the slope without taking into account friction forces occurs under the influence of gravity, which refers to conservative forces, i.e. The law of conservation of energy is valid:
E 1 = E 2 ; K 1 + P 1 = K 2 + P 2;
2. At starting point 1, the sled has kinetic and potential energy. If the level at the base of the mountain is taken to be the zero level of potential energy, then the potential energy at the end of the descent will be zero. In this case, the law of conservation of energy will take the form:
Mgh = |
; v1 2 + 2gh = v2 2 ; |
− v 2 |
225 − 25 |
≈ 10m; |
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1. The speed of sound c in media, without taking into account dispersion (the dependence of the speed of elastic waves on frequency) is equal to the product of frequency ν and wavelength λ:
c = λ1 ν1 = λ2 ν2 ; λ1 λ2 = ν2 ν1 = 4;
A7. As a result of cooling of an ideal gas, the average kinetic energy of thermal motion of its molecules decreased by three times. How many times did the absolute temperature of this ideal gas change?
1. An ideal gas molecule has three translational degrees of freedom i = 3, therefore the kinetic energy of translational motion, in accordance with the basic equation of molecular kinetic theory, is determined by the equation:
< ε >= 2 i k B T = 3 2 k B T ,
where kB is the Ludwig Boltzmann constant, T is the absolute temperature.
2. Kinetic energy of ideal gas molecules in two given states:
; T3 |
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< ε 1 > = |
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A8. One mole of rarefied gas was first compressed isothermally and then heated isochorically. Which of the figures shows a graph of these processes?
1. To answer the question posed, it is necessary to depict isoprocesses
V various combinations of state parameters:
2. Comparison of graphs taking into account the sequence of processes (first, at a constant temperature, the gas was compressed, i.e., its pressure was increased, and then, at a constant pressure, it was heated); graph 2 corresponds to the given course of processes.
A9. Water can evaporate:
1. Only when boiling;
2. Only when heated;
3. At any temperature, if the vapor above the surface of the water is unsaturated;
4. At any temperature, if the vapor in the air above the surface of the water is saturated?
1. In the liquid state, the molecules of substances mainly perform oscillatory movements, but some of the molecules, as a result of the interaction between neighbors, receive a translational component of motion; it is these molecules, being located in the surface layer of the liquid, that are able to overcome the forces of surface tension and leave the liquid, turning into its vapor.
2. In principle, the evaporation process occurs at any temperature, if the vapor above the surface is unsaturated, when a state of saturation occurs, the number of molecules leaving a unit surface of the liquid per unit time becomes equal to the number of liquids returning to the liquid during the condensation process, in this case they speak of a state of dynamic equilibrium between liquid and vapor state.
3. Thus, the amount of substance in the liquid state will decrease due to evaporation in all cases until the vapor pressure reaches its saturation value.
A10. The gas did work A = 10 J and received an amount of heat Q = 6 J. Internal energy of the gas U:
1. Increased by 16 J;
2. Decreased by 16 J?
3. Increased by 4 J;
4. Decreased by 4 J?
1. In accordance with the first law of thermodynamics:
δ Q = δ A + U; U = 6 − 10 = − 4J;
The internal energy of the gas decreased by 4 J.
A11. Two stationary point electric charges exert a modulus of forces on each other with forces equal in modulus to 9 µN. What will the modulus of interaction forces between charges become if, without changing the distance between them, the modulus of each of them is increased by 3 times?
1. The interaction of point electric charges obeys Coulomb’s law:
4 πεε0 |
81μN; |
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4 πεε0 |
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A12. Two resistors are connected in an electrical circuit in parallel, with I1 = 0.8 A, I2 = 0.2 A. For the resistances of the resistors, the following relation is true:
1. Resistors are connected in parallel, so the voltage drop across them will be the same, which makes it possible to apply the consequences of Ohm’s law to a section of the circuit:
U = I |
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A13. Michael Faraday's fundamental law of electromagnetic induction
εi = − Φ t B
can be explained:
1. The interaction of two parallel wires carrying current;
2. Deviation of a magnetic needle located near a conductor with current parallel to it;
3. The appearance of an electric current in a closed coil when the current increases in another coil located nearby;
4. The occurrence of a force acting on a current-carrying conductor in a magnetic field
1. Manifestation of the law of electromagnetic
The third case corresponds to induction. Experimental confirmation of which can be a transformer connected to an alternating current circuit, where in the circuit of the first coil the current strength changes according to a sinusoidal law, i.e. the flux of magnetic induction changes according to a sinusoidal law
Φ B (t ) = Φ B(max) sin ω t;
A14. The voltage on the capacitor plates in the oscillating circuit changes over time in accordance with the given graph. What a transformation
1 = 2 10 − 6 s to t2
3 10 −6 s?
1. The coil's magnetic field energy decreases from its maximum value to zero;
2. The energy of the magnetic field of the coil is converted into the energy of the electric field of the capacitor;
3. The energy of the capacitor's electric field increases from zero to a maximum value;
4. The energy of the electric field of the capacitor is converted into the energy of the magnetic field of the capacitor;
1. The energy of a charged capacitor is determined by the equation:
(t)= |
Cu(t)2 |
||
those. in a specified period of time, the energy of the capacitor changes from a certain amplitude value to zero.
2. In accordance with the law of conservation of electromagnetic energy, a decrease in the energy of the electric field of the capacitor must be accompanied by an increase in the magnetic field of the coil, i.e. In a given time interval, the process of converting electrical energy into magnetic energy occurs.
A15. The figure shows the path of a light beam through a glass prism in the air. If point O is the center of the circle, then the refractive index of glass n is equal to the ratio of the lengths of the segments:
1. The law of light refraction for the case under consideration will be written as follows:
sin α |
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OA = OC; |
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sinβ |
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A16. In an inertial reference frame, light from a stationary source propagates in a vacuum with a speed c. If the source and the mirror move towards each other with velocities equal in magnitude v, then the speed of the reflected ray of light in the inertial reference frame associated with the source is equal to:
1. c − 2v; 2.c; 3. c + 2v; 4. c 1− |
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Four bodies moved along the Ox axis. The table shows the dependence of their coordinates on time.
Which body could have a constant velocity and different from zero?
1) - 1 2) - 2 3) - 3 4) - 4
Task 2
Two forces act on a body in an inertial frame of reference. Which of the vectors shown in the right figure correctly indicates the direction of acceleration of the body in this reference frame?
1) - 1 2) - 2 3) - 3 4) - 4
Task 3
The figure shows a graph of the dependence of the modulus of elastic force on the elongation of the spring. What is the spring stiffness?
1) 250 N/m
2) 160 N/m
3) 2.5 N/m
4) 1.6 N/m
Task 4
Two bodies move along mutually perpendicular intersecting lines, as shown in the figure. The modulus of the first body is p 1 = 4 kg⋅m/s, and the second body is p 2 = 3 kg*m/s. What is the modulus of momentum of the system of these bodies after their absolutely inelastic impact?
1) 1 kg⋅m/s 2) 4 kg⋅m/s 3) 5 kg⋅m/s 4) 7 kg⋅m/s
Task 5
A car weighing 10 3 kg moves at a speed of 10 m/s. What is the kinetic energy of the car?
1) 105 J 2) 104 J 3) 5⋅104 J 4) 5⋅103 J
Task 6
The period of oscillation of a spring pendulum is 1 s. What will be the period of oscillation if the mass of the pendulum's load and the stiffness of the spring are increased by 4 times?
1) 1 s 2) 2 s 3) 4 s 4) 0.5 s
Task 7
On the last kilometer of the braking distance, the speed of the train decreased by 10 m/s. Determine the speed at the beginning of braking if the total braking distance of the train was 4 km, and the braking was uniformly slow.
1) 20 m/s 2) 25 m/s 3) 40 m/s 4) 42 m/s
Task 8
As the temperature of the gas in the sealed vessel decreases, the gas pressure decreases. This decrease in pressure is due to the fact that
1) the energy of thermal motion of gas molecules decreases
2) the energy of interaction of gas molecules with each other decreases
3) the randomness of the movement of gas molecules decreases
4) the size of gas molecules decreases as it cools
Task 9
On the gas stove there is a narrow saucepan with water, closed with a lid. If you pour water from it into a wide pan and also close it, the water will boil noticeably faster than if it remained in a narrow one. This fact is explained by the fact that
1) the heating area increases and, therefore, the rate of water heating increases
2) the required saturated vapor pressure in the bubbles increases significantly and, therefore, the water at the bottom must be heated to a lower temperature
3) the surface area of water increases and, therefore, evaporation occurs more actively
4) the depth of the water layer noticeably decreases and, therefore, steam bubbles reach the surface faster
Task 10
The relative humidity of the air in the cylinder under the piston is 60%.
The air was isothermally compressed, reducing its volume by half. The relative air humidity became equal to
1) 120% 2) 100% 3) 60% 4) 30%
Task 11
Four metal bars were placed close to each other, as shown in the figure. The arrows indicate the direction of heat transfer from block to block. Bar temperatures are currently 100°C, 80°C, 60°C, 40°C.
The bar has a temperature of 60°C
1) A 2) B 3) C 4) D
Task 12
At a temperature of 10°C and a pressure of 10 3 Pa, the gas density is 2.5 kg/m3.
What is the molar mass of the gas?
1) 59 g/mol 2) 69 g/mol 3) 598 kg/mol 4) 5.8 10-3 kg/mol
Task 13
An uncharged metal body was introduced into a uniform electrostatic field and then divided into parts A and B (see figure). What electrical charges do these parts have after separation?
1) A – positive, B – will remain neutral
2) A – will remain neutral, B – negative
3) A – negative, B – positive
4) A – positive, B – negative
Task 14
A constant electric current flows through a conductor. The value of the charge passing through the conductor increases over time according to the graph presented in the figure.
The current strength in the conductor is equal to
1) 36 A 2) 16 A 3) 6 A 4) 1 A
Task 15
The inductance of a wire turn is 2⋅10–3 H. At what current strength in the coil is the magnetic flux through the surface bounded by the coil equal to 12 mWb?
1) 24⋅10–6 A 2) 0.17 A 3) 6 A 4) 24 A
Task 16
The figure shows the induction vector in the Cartesian coordinate system B magnetic field in electromagnetic wave and vector c the speed of its spread. Direction of the electric field strength vector E in the wave coincides with the arrow 
1) 1 2) 2 3) 3 4) 4
Task 17
Students investigated the relationship between the speeds of a car and its image in a plane mirror in the reference frame associated with the mirror (see figure).
Projection on the O axis X the speed vector with which the image moves in this reference system is equal to
1) – 2υ 2) 2υ 3) υ 4) – υ
Task 18
Two point light sources S 1 and S 2 are close to each other and create a stable interference pattern on the remote screen E (see figure).
This is possible if S1 and S2 are small holes in an opaque screen, illuminated
1) each with its own sunbeam from different mirrors
2) one - with an incandescent light bulb, and the second - with a burning candle
3) one with blue light and the other with red light
4) light from the same point source
Task 19
Two point positive charges q 1 = 200 nC and q 2 = 400 nC are in a vacuum. Determine the magnitude of the electric field strength of these charges at point A, located on the straight line connecting the charges, at a distance L from the first and 2L from the second charge. L = 1.5 m.
1) 1200 kV/m 2) 1200 V/m 3) 400 kV/m 4) 400 V/m
Task 20
The figure shows several of the lowest energy levels of the hydrogen atom. Can an atom in the E 1 state absorb a photon with an energy of 3.4 eV?
1) yes, in this case the atom goes into state E 2
2) yes, in this case the atom goes into state E 3
3) yes, in this case the atom is ionized, decaying into a proton and an electron
4) no, the photon energy is not enough for the atom to transition to an excited state
Task 21
What fraction of radioactive nuclei decays after a time interval equal to two half-lives?
1) 100% 2) 75% 3) 50% 4) 25%
Task 22
Radioactive polonium 84 216 Po, having undergone one α-decay and two β-decays, turned into an isotope
1) lead 82 212 Pb
2) polonium 84 212 Po
3) bismuth 83 212 Bi
4) thallium 81 208 PTl
Task 23
One way to measure Planck's constant is based on determining the maximum kinetic energy of electrons during the photoelectric effect by measuring the voltage that retards them. The table shows the results of one of the first such experiments.
Planck's constant according to the results of this experiment is equal to
1) 6.6⋅10 -34 J⋅s 2) 5.7⋅10 -34 J⋅s 3) 6.3⋅10 -34 J⋅s 4) 6.0⋅10 -34 J⋅s
Task 24
When measuring the current in a coil of wire R, four students connected the ammeter in different ways. The result is shown in the figure. Indicate the correct ammeter connection.
Answers to the physics test, grade 11
| Quests | Answer | Quests | Answer |
| 1 | 1 | 14 | 4 |
| 2 | 3 | 15 | 3 |
| 3 | 1 | 16 | 2 |
| 4 | 3 | 17 | 4 |
| 5 | 3 | 18 | 4 |
| 6 | 1 | 19 | 4 |
| 7 | 1 | 20 | 4 |
| 8 | 1 | 21 | 2 |
| 9 | 1 | 22 | 2 |
| 10 | 2 | 23 | 2 |
| 11 | 2 | 24 | 3 |
| 12 | 1 | ||
| 13 | 4 |
Problems with solutions for preparing for the Unified State Exam.
To complete the examination work in physics, 4 hours (240 minutes) are allotted. The work consists of 3 parts, including 35 tasks.
- Part 1 contains 25 tasks (A1-A25). For each task there are 4 possible answers, of which only one is correct.
- Part 2 contains 4 tasks (B1-B4), in which the answer must be written down as a set of numbers.
- Part 3 consists of 6 tasks (C1-C6), for which detailed solutions are required.
When making calculations, it is allowed to use a non-programmable calculator.
Read each task carefully and the suggested answer options, if any. Answer only after you understand the question and have considered all possible answers. Complete the tasks in the order in which they are given. If a task is difficult for you, skip it. You can return to missed tasks if you have time. The points you receive for completed tasks are summed up. Try to complete as many tasks as possible and score the most points.
Below is reference information that you may need when doing the job.
Decimal prefixes
Naimenov | Designate | Factor- | Naimenov | Designate | Factor- |
| Milli | |||||
PART 1
When completing tasks in Part 1, in answer form No. 1, under the number of the task you are performing (A1-A25), put the “×” sign in the box whose number corresponds to the number of the answer you chose.
A1 Four bodies moved along the Ox axis. The table shows the dependence of their coordinates on time.
Which body could have a constant velocity and different from zero?
1) 1 2) 2 3) 3 4) 4
A2 Two forces act on a body in an inertial frame of reference. Which of the vectors shown in the right figure correctly indicates the direction of acceleration of the body in this frame of reference?
1) 1 2) 2 3) 3 4) 4
A3 The figure shows a graph of the dependence of the modulus of elastic force on the elongation of the spring. What is the spring stiffness?
A4 Two bodies move along mutually perpendicular intersecting lines, as shown in the figure. The modulus of the first body is p1 = 4 kg⋅m/s, and the second body is p2 = 3 kg⋅m/s. What is the modulus of momentum of the system of these bodies after their absolutely inelastic impact?
1) 1 kg⋅ m/s
2) 4 kg m/s
3) 5 kg⋅m/s
4) 7 kg⋅m/s
A5 A car weighing 103 kg moves at a speed of 10 m/s. What is the kinetic energy of the car?
1) 10 5 J
2) 10 4 J
3) 5⋅10 4 J
4) 5⋅10 3 J
A6 The period of oscillation of a spring pendulum is 1 s. What will be the period of oscillation if the mass of the pendulum's load and the stiffness of the spring are increased by 4 times?
1) 1 s
2) 2 s
3) 4 s
4) 0.5 s
A7 On the last kilometer of the braking distance, the speed of the train decreased by 10 m/s. Determine the speed at the beginning of braking if the total braking distance of the train was 4 km, and the braking was uniformly slow.
1) 20 m/s
2) 25 m/s
3) 40 m/s
4) 42 m/s
A8 When the gas temperature in a sealed vessel decreases, the gas pressure decreases. This decrease in pressure is due to the fact that
1) the energy of thermal motion of gas molecules decreases
2) the energy of interaction of gas molecules with each other decreases
3) the randomness of the movement of gas molecules decreases
4) the size of gas molecules decreases as it cools
A9 There is a narrow pan of water on the gas stove, covered with a lid. If you pour water from it into a wide pan and also close it, the water will boil noticeably faster than if it remained in a narrow one. This fact is explained by the fact that
1) the heating area increases and, therefore, the rate of water heating increases
2) the required saturated vapor pressure in the bubbles increases significantly and, therefore, the water at the bottom must be heated to a lower temperature
3) the surface area of water increases and, therefore, evaporation occurs more actively
4) the depth of the water layer noticeably decreases and, therefore, steam bubbles reach the surface faster
A10 The relative humidity of the air in the cylinder under the piston is 60%. The air was isothermally compressed, reducing its volume by half. The relative air humidity became equal to
1) 120%
2) 100%
3) 60%
4) 30%
A11 Four metal bars were placed close to each other, as shown in the figure. The arrows indicate the direction of heat transfer from block to block. Bar temperatures are currently 100°C, 80°C, 60°C, 40°C. The bar has a temperature of 60°C
1) A
2) B
3) C
4) D
A12 At a temperature of 10°C and a pressure of 10 5 Pa, the gas density is 2.5 kg/m 3. What is the molar mass of the gas?
1) 59 g/mol
2) 69 g/mol
3) 598 kg/mol
4) 5.8-10 -3 kg/mol
A13 An uncharged metal body was introduced into a uniform electrostatic field, and then divided into parts A and B (see figure). What electrical charges do these parts have after separation?
1) A - positive, B - will remain neutral
2) A - will remain neutral, B - negative
3) A - negative, B - positive
4) A - positive, B - negative
A14 A direct electric current flows through a conductor. The value of the charge passing through the conductor increases over time according to the graph presented in the figure. The current strength in the conductor is equal to
1) 36 A
2) 16 A
3) 6 A
4) 1 A
A15 The inductance of a turn of wire is 2⋅10 -3 H. At what current strength in the coil is the magnetic flux through the surface bounded by the coil equal to 12 mWb?
1) 24⋅10 -6 A
2) 0.17 A
3) 6 A
4) 24 A
A16 The figure shows the induction vector B → magnetic field in an electromagnetic wave and the vector in the Cartesian coordinate system c→ the speed of its spread. The direction of the electric field strength vector E → in the wave coincides with the arrow
1) 1
2) 2
3) 3
4) 4
A17 Students investigated the relationship between the speeds of a car and its image in a plane mirror in the reference frame associated with the mirror (see figure). Projection onto the axis Oh the speed vector with which the image moves in this reference system is equal to
1) - 2v
2) 2v
3) v
4) - v
A18 Two point light sources S 1 and S 2 are close to each other and create a stable interference pattern on the remote screen E (see figure). This is possible if S 1 and S 2 are small holes in an opaque screen, illuminated
1) each with its own sunbeam from different mirrors
2) one - an incandescent light bulb, and the second - a burning candle
3) one with blue light and the other with red light
4) light from the same point source
A19 Two point positive charges q 1= 200 nC and q 2= 400 nC are in vacuum. Determine the magnitude of the electric field strength of these charges at point A, located on a straight line connecting the charges, at a distance L from the first and 2L from the second charge. L= 1.5 m.
1) 1200 kV/m
2) 1200 V/m
3) 400 kV/m
4) 400 V/m
A20 The figure shows several of the lowest energy levels of the hydrogen atom. Can an atom in a state E 1, absorb a photon with an energy of 3.4 eV?
1) yes, in this case the atom goes into the state E 2
2) yes, in this case the atom goes into the state E 3
3) yes, in this case the atom is ionized, decaying into a proton and an electron
4) no, the photon energy is not enough for the atom to transition to an excited state
A21 What fraction of radioactive nuclei decays after a time interval equal to two half-lives?
1) 100%
2) 75%
3) 50%
4) 25%
A22 Radioactive polonium, having undergone one α-decay and two β-decays, turned into an isotope
1) lead 2) polonium 3) bismuth 4) thallium
A23 One way to measure Planck's constant is based on determining the maximum kinetic energy of electrons during the photoelectric effect by measuring the voltage that retards them. The table shows the results of one of the first such experiments.
Holding voltage U, V | ||
Light frequency v, 10 14 Hz |
Planck's constant according to the results of this experiment is equal to
1) 6.6⋅10 -34 J⋅s
2) 5.7⋅10 -34 J⋅s
3) 6.3⋅10 -34 J⋅s
4) 6.0⋅10 -34 J⋅s
A24 When measuring current in a spiral wire R four students connected the ammeter in different ways. The result is shown in the figure. Indicate the correct ammeter connection.
A25 When conducting an experiment, the student investigated the dependence of the modulus of the elastic force of the spring on the length of the spring, which is expressed by the formula F(l) = k|l − l 0 | , Where l 0- length of the spring in an undeformed state.
The graph of the obtained dependence is shown in the figure.
Which of the statements correspond(s) to the results of the experiment?
A. The undeformed length of the spring is 3 cm.
B. The spring stiffness is 200 N/m.
1) only A
2) only B
3) both A and B
4) neither A nor B
PART 2
The answer to the tasks in this part (B1-B4) is a sequence of numbers. Enter the answers first into the text of the work, and then transfer them to answer form No. 1 to the right of the number of the corresponding task, starting from the first cell, without spaces or any additional characters. Write each number in a separate box in accordance with the samples given in the form.
B1 As a result of the transition from one circular orbit to another, the centripetal acceleration of the Earth's satellite decreases. How do the satellite’s orbital radius, its orbital speed, and its orbital period around the Earth change as a result of this transition? For each quantity, determine the corresponding nature of the change:
1) increased
2) decreased
3) has not changed
B2 The temperature of the heat engine refrigerator was increased, leaving the heater temperature the same. The amount of heat received by the gas from the heater per cycle has not changed. How did the efficiency of the heat engine, the amount of heat transferred by the gas per cycle to the refrigerator, and the work of the gas per cycle change?
For each quantity, determine the corresponding nature of the change:
1) increased
2) decreased
3) has not changed
Write down the selected numbers for each physical quantity in the table. The numbers in the answer may be repeated.
B3 A beam of light passes from water to air. The frequency of the light wave is ν, the speed of light in water is v, the refractive index of water relative to air - n. Establish a correspondence between physical quantities and formulas by which they can be calculated. For each position in the first column, select the corresponding position in the second and write down the selected numbers in the table under the corresponding letters.
| A | B |
B4 
The oscillating circuit capacitor is connected to a constant voltage source (see figure). Graphs A and B represent changes in physical quantities characterizing oscillations in the circuit after switch K is moved to position 2. Establish a correspondence between the graphs and the physical quantities, the dependence of which on time these graphs can represent. For each position in the first column, select the corresponding position in the second and write down the selected numbers in the table under the corresponding letters.
| A | B |
Do not forget to transfer all answers to answer form No. 1.
PART 3
Tasks C1-C6 are problems, the complete solution of which must be written down in answer form No. 2. It is recommended to carry out a preliminary solution on a draft. When completing the solution in answer form No. 2, first write down the task number (CI, C2, etc.), and then the solution to the corresponding problem. Write down your answers clearly and legibly.
C1
A complete correct solution to each of the problems C2-C6 must include laws and formulas, the use of which is necessary and sufficient to solve the problem, as well as mathematical transformations, calculations with a numerical answer and, if necessary, a drawing explaining the solution.
C2 Puck mass m N m
C3 p 1= 4·10 5 Pa. The distance from the bottom of the vessel to the piston is L S= 25 cm 2. As a result of slow heating, the gas received an amount of heat Q= 1.65 kJ, and the piston has moved a distance x F tr = 3 10 3 N. Find L
C4 During laboratory work, the student assembled an electrical circuit according to the diagram in the figure. Resistance R 1 and R 2 are equal to 20 Ohms and 150 Ohms respectively. The resistance of a voltmeter is 10 kOhm, and that of an ammeter is 0.4 Ohm. The emf of the source is 36 V, and its internal resistance is 1 Ohm.
C5
C6 t= 8·10 -4 s emits N S P
Assessment system for examination work in physics
PART1
For the correct answer to each task in Part 1, 1 point is given. If two or more answers are indicated (including the correct one), an incorrect answer or no answer - 0 points.
Job No. | Answer | Job No. | Answer |
PART 2
A task with a short answer is considered completed correctly if the sequence of numbers is correctly indicated in tasks B1-B4.
For a complete correct answer, 2 points are given, 1 point - one mistake was made; for an incorrect answer (more than one error) or absence of one - 0 points.
Job No. | Answer |
PART 3
CRITERIA FOR EVALUATING COMPLETION OF TASKS WITH DETAILED ANSWER
C1 The figure shows an electrical circuit consisting of a galvanic element, a rheostat, a transformer, an ammeter and a voltmeter. At the initial moment of time, the rheostat slider is installed in the middle and motionless. Based on the laws of electrodynamics, explain how instrument readings will change as the rheostat slider moves to the left. Neglect self-induction emf compared to ε.
Sample possible solution |
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1. While moving the rheostat slider, the ammeter readings will gradually increase, and the voltmeter will record the voltage at the ends of the secondary winding. Note: An explanation of the instrument readings at the far left is not required for a complete answer. (When the engine reaches the extreme left position and its movement stops, the ammeter will show a constant current in the circuit, and the voltage measured by the voltmeter will be zero.) 2. As the slider moves to the left, the circuit resistance decreases and the current increases in accordance with Ohm's law for a complete circuit 3. A change in the current flowing through the primary winding of the transformer causes a change in the induction of the magnetic field created by this winding. This causes a change in the magnetic flux through the secondary winding of the transformer. 4. In accordance with Faraday’s law of induction, an induced emf occurs | |
Points |
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A complete correct solution is given, including the correct answer (in this case - a change in instrument readings, point 1), and a complete correct explanation (in this case - points 2-4) indicating the observed phenomena and laws (in this case - electromagnetic induction , Faraday's law of induction, Ohm's law for a complete circuit). | 3 |
The solution is given and the correct answer is given, but there is one of the following shortcomings: The explanation contains only general reasoning without reference to the specific situation of the problem, although all the necessary physical phenomena and laws are indicated; | 2 |
Reasoning is given indicating physical phenomena and laws, but an incorrect or incomplete answer is given; | 1 |
| 0 | |
Where R- resistance of the external circuit.
in the secondary winding, and therefore the voltage U at its ends, recorded by a voltmeter.C2 Puck mass m begins to move along the channel AB from point A from a state of rest. Point A is located above point B at a height N= 6 m. During movement along the chute, the mechanical energy of the washer due to friction decreases by ΔE = 2J. At point B, the puck flies out of the chute at an angle α = 15° to the horizontal and falls to the ground at point D, located on the same horizontal line as point B (see figure). BD = 4 m. Find the mass of the washer m. Neglect air resistance.
Sample possible solution |
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1. The speed of the puck at point B is determined from the balance of its energy at points A And IN taking into account friction losses:
From here: 2. Time of flight of the puck from the point IN to the point D:
reference with the origin at the point IN. 3. The flight range BD is determined from the expression for the horizontal coordinates of the puck in the same reference system: 4. Substituting into the expression for BD meaning v 2, we get
5. From here we find the mass of the washer: Answer: m= 0.1 kg. |
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Criteria for assessing assignment completion | Points |
The complete correct solution is given, including the following elements: The use of which is necessary to solve the problem in the chosen way (in this solution - the law of conservation of energy and formulas for the kinematics of free fall); 2) the necessary mathematical transformations and calculations leading to the correct numerical answer are carried out, and the answer is presented; in this case, a solution “in parts” is allowed (with intermediate calculations). | |
| 2 |
Records are presented that correspond to one of the following cases:
| 1 |
| 0 | |
Where y- vertical coordinate of the washer in the system
C3 A monatomic ideal gas is contained in a horizontal cylindrical vessel closed by a piston. Initial gas pressure p 1 = 4·10 5 Pa. The distance from the bottom of the vessel to the piston is L. Piston cross-sectional area S= 25 cm 2. As a result of slow heating, the gas received an amount of heat Q = 1.65 kJ, and the piston moved a distance x= 10 cm. When the piston moves, a frictional force of magnitude acts on it from the side of the walls of the vessel F tr = 3 10 3 N. Find L. Assume that the vessel is in a vacuum.
Sample possible solution |
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1. The piston will move slowly if the force of gas pressure on the piston and the friction force from the walls of the vessel balance each other: p 2 S = F tr,
2. Therefore, when the gas is heated, the piston will remain motionless until the gas pressure reaches the value p 2. In this process, the gas receives an amount of heat Q 12. Q = Q 12 +Q 23 = (U 3 −U 1) + p 2 Sx = (U 3 −U 1) + F tr x. 4) Internal energy of a monatomic ideal gas:
in the final state. 5) From paragraphs. 3, 4 we get Answer: L= 0.3 m. |
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Criteria for assessing assignment completion | Points |
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— an error was made in the necessary mathematical transformations or calculations; | |
Records are presented that correspond to one of the following cases: — Only provisions and formulas expressing physical laws, the application of which is necessary to solve the problem, are presented, without any transformations with their use aimed at solving the problem and the answer; | |
All cases of solution that do not correspond to the above | |
in its initial state,
C4 During laboratory work, the student assembled an electrical circuit according to the diagram in the figure. Resistances R 1 and R 2 are 20 Ohms and 150 Ohms, respectively. The resistance of a voltmeter is 10 kOhm, and that of an ammeter is 0.4 Ohm. The emf of the source is 36 V, and its internal resistance is 1 Ohm.
The figure shows the instrument scales with the readings that the student received. Are the instruments working properly or are some of them giving incorrect readings?
Sample possible solution |
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To determine the current strength, we use Ohm's law for a complete circuit. The voltmeter and resistor R 1 are connected in parallel. Hence, The ammeter shows a current strength of about 0.22 A. The ammeter scale division value is 0.02 A, which is greater than the deviation of the readings from the calculation. Hence, The ammeter gives correct readings. From here U = I ⋅ R 1 = 0.21⋅20 = 4.2 (V). The voltmeter shows the voltage |
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Criteria for assessing assignment completion | Points |
The complete correct solution is given, including the following elements: 1) correctly written formulas expressing physical laws, the application of which is necessary to solve the problem in the chosen way (in this solution - Ohm’s law for the complete circuit and for a section of the circuit, formulas for calculating the resistance of a section of a circuit for series and parallel connection of conductors); 2) the necessary mathematical transformations and calculations leading to the correct numerical answer are carried out, and the answer is presented. In this case, a solution is allowed “in parts” (with intermediate calculations). | |
The presented solution contains paragraph 1 of the complete solution, but also has one of the following disadvantages: There was an error in the required mathematical transformations or calculations; | |
Records are presented that correspond to one of the following cases: Only provisions and formulas expressing physical laws, the application of which is necessary to solve the problem, are presented, without any transformations with their use aimed at solving the problem and the answer; | |
All cases of solution that do not meet the above criteria for scoring 1, 2, 3 points. | |
C5 A small load suspended on a thread 2.5 m long undergoes harmonic oscillations, at which its maximum speed reaches 0.2 m/s. Using a converging lens with a focal length of 0.2 m, the image of an oscillating mass is projected onto a screen located at a distance of 0.5 m from the lens. The main optical axis of the lens is perpendicular to the plane of oscillation of the pendulum and the plane of the screen. Determine the maximum displacement of the load image on the screen from the equilibrium position.
Sample possible solution |
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When the pendulum oscillates, the maximum speed of the load is v can be determined from the law of conservation of energy: maximum lifting height. Maximum deflection angle where A- amplitude of oscillations (amplitude of displacement). From here Amplitude A 1 oscillation of the displacement of the cargo image on a screen located at a distance b from the plane of a thin lens, proportional to the amplitude A vibrations of a load moving at a distance A from the plane of the lens: Distance a is determined by the thin lens formula: Hence,
Answer: A 1 = 0.15 m. |
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Criteria for assessing assignment completion | Points |
The complete correct solution is given, including the following elements: 1) formulas expressing physical laws are written correctly, the use of which is necessary to solve the problem in the chosen way (in this solution - the law of conservation of energy, the formula for magnifying a thin lens and the formula for a thin lens); 2) the necessary mathematical transformations and calculations leading to the correct numerical answer are carried out, and the answer is presented. In this case, a solution is allowed “in parts” (with intermediate calculations). | |
The presented solution contains point 1 of the complete solution, but also has one of the following disadvantages: There was an error in the required mathematical transformations or calculations; | |
Records are presented that correspond to one of the following cases: Only provisions and formulas expressing physical laws, the application of which is necessary to solve the problem, are presented, without any transformations with their use aimed at solving the problem and the answer; | |
All cases of solution that do not correspond to the above | |
where 
C6 A monochromatic beam of parallel rays is created by a source, which, in a time Δ t= 8·10 -4 s emits N= 5·10 14 photons. Photons fall normally onto the site S= 0.7 cm 2 and create pressure P= 1.5·10 -5 Pa. In this case, 40% of photons are reflected, and 60% are absorbed. Determine the wavelength of the radiation.
Sample possible solution |
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Expression for light pressure: (Formula (1) follows from.) Formulas for changing the momentum of a photon during reflection and absorption of rays: Expression for photon momentum: Expression for the radiation wavelength: |
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Criteria for assessing assignment completion | Points |
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The complete correct solution is given, including the following elements: 1) formulas expressing physical laws are written correctly, the use of which is necessary to solve the problem using the chosen method (in this solution - formulas for light pressure, photon momentum, Newton's II law); 2) the necessary mathematical transformations and calculations leading to the correct numerical answer are carried out, and the answer is presented. In this case, a solution is allowed “in parts” (with intermediate calculations). | |||
The presented solution contains paragraph 1 of the complete solution, but also has one of the following disadvantages: There was an error in the required mathematical transformations or calculations; | |||
Records are presented that correspond to one of the following cases: Only provisions and formulas expressing physical laws, the application of which is necessary to solve the problem, are presented, without any transformations with their use aimed at solving the problem and the answer; | |||
All cases of solution that do not correspond to the above | |||
