Class 11 Physics Past Paper PDF 2021-2022

# CLASS-XI PHYSICS (THEORY) (042) ANNUAL EXAM (2021-22) ## General Instructions: 1. All questions are compulsory. There are 19 questions in all. 2. This question paper has five sections: Section A, Section B, Section C, Section D and Section E. 3. Section A contains five questions of 1 mark each....

# CLASS-XI PHYSICS (THEORY) (042) ANNUAL EXAM (2021-22) ## General Instructions: 1. All questions are compulsory. There are 19 questions in all. 2. This question paper has five sections: Section A, Section B, Section C, Section D and Section E. 3. Section A contains five questions of 1 mark each. Section B contains seven questions of 2 marks each. Section C contains four questions of 3 marks each. Section D contains one case-based problem of four marks. Section E contains two questions of five marks each. 4. There is no overall choice. However, an internal choice is provided in one question of one mark, three questions of two marks, two questions of three marks, one internal choice in case study based question and all questions of five marks weightage. You have to attempt only one of the choice in such questions. 5. Fifteen minutes time has been allotted to read this question paper. During this time the student will only read the question paper and will not write any answer on the answer sheet. 6. Use log table, if necessary. ## Section-A Questions 1-5 are Assertion and Reason type questions. Select the most appropriate answer from the options given below: (a) Both Assertion (A) and Reason (R) are correct and R is the correct explanation of A. (b) Both Assertion (A) and Reason (R) are correct and R is not the correct explanation of A. (c) Assertion (A) is true but Reason (R) is false. (d) Assertion (A) is false and Reason (R) is also false. 1. **Assertion (A):** The centripetal acceleration of a particle in uniform circular motion is not a constant vector. **Reason (R):** The magnitude of the centripetal acceleration is constant but its direction changes, pointing always towards the centre. 2. **Assertion (A):** The work done by a spring force in a cyclic process is zero. **Reason (R):** The spring force is a non-conservative force. 3. **Assertion (A):** Internal energy of an ideal gas does not depend upon the volume of the gas. **Reason (R):** Internal energy of an ideal gas depends on temperature of the gas. **OR** **Assertion (A):** In an adiabatic process, the heat absorbed or released by an ideal gas is zero. **Reason (R):** The work done by the gas results in increase in its temperature. 4. **Assertion (A):** The graph between total energy of a particle in simple harmonic motion and its displacement is a straight line parallel to displacement axis. **Reason (R):** Total energy of particle in SHM remains constant throughout its motion. 5. **Assertion (A):** The average kinetic energy of a molecule of a gas is directly proportional to the square root of the absolute temperature of the gas. **Reason (R):** The average kinetic energy of a molecule of a gas is dependent on pressure of the gas. ## Section-B 6. Show that the pressure of an ideal gas is directly proportional to the square of speed of its molecules. **OR** Show that the ratio of specific heats (C_p/C_v) is equal to 5/3 for an ideal monatomic gas. 7. Obtain an expression for gravitational potential energy of two masses separated by a distance. **OR** Show that a path of a projectile, neglecting air resistance, is parabolic. 8. Show that the speed of sound in air is directly proportional to the square root of the ratio of two specific heats (C_p/C_v). **OR** Two harmonic sound waves of equal amplitude, same phase and of nearly equal angular frequencies ω₁ and ω₂ super-impose and form beats. Show that the resultant wave oscillates with angular frequency (ω₁ + ω₂)/2 and its amplitude is not constant in time. (Take x = 0 for each wave) y = A sin(ω₁t) + A sin(ω₂t) = 2A cos [(ω₁ - ω₂)/2]t sin [(ω₁ + ω₂)/2]t Draw diagrams to show first two harmonics in (i) an open organ pipe and (ii) a closed organ pipe. 10. Figure shows a composite cylindrical bar made of two metals A and B. The coefficient of thermal conductivity of metal A is nine times that of B. What will be the temperature at the junction of metals A and B ? ![Figure showing two metals A and B connected, with temperature of 100°C at one end and 0°C at the other end. Metal A is 10 cm long and metal B is 6 cm long.] 11. Calculate the change in internal energy when 1 g of water goes from liquid to vapour phase. (Latent heat of water = 2256 J/g, volume of 1 g of water in vapour phase = 1671 cm³ and 1 atm pressure = 1.01 x 10⁵ Pa). 12. A body is in rotational equilibrium but not in translational equilibrium. Explain it with an example. ## Section-C 13. Figure shows four forces acting on a particle P, which is at rest. Find the magnitudes of the forces F₁ and F₂. ![Diagram showing a particle P at equilibrium with forces acting with different directions and magnitudes.] 14. Show that the terminal velocity (v_t) of a spherical body of radius (r), density (ρ) falling vertically through a viscous fluid of density (σ) and coefficient of viscosity (η) is given by v_t = 2(ρ - σ) g r² / 9η . 15. A spring having spring constant 1200 N/m is mounted on a horizontal table as shown in the figure. A mass of 3 kg is attached to the free end of the spring pulled sideways to a distance of 2 cm and released. Calculate- (a) the frequency of oscillation (b) maximum acceleration (c) maximum speed of the mass ![A spring is shown attached to a mass of 3 kg.] **OR** A body oscillate with SHM according to the equation x = 4 cos (πt + π/3) where x is in metres and t is in seconds. Calculate (a) displacement, (b) speed (c) acceleration of the body, at t = 1.5s 16. Derive an expression for the work done by an ideal gas when it expands isothermally from volume V₁ to V₂ at temperature T. Hence show that the heat supplied to the gas equals the work done by the gas, in an isothermal process. **OR** Derive an expression for the work done by an ideal gas in an adiabatic change of state from (P₁, V₁, T₁) to (P₂, V₂, T₂). ## Section-D 17. A wire of length 2L and radius r, made of material of Young's modulus Y is stretched and held straight horizontally without tension between points A and B. A body of mass M, suspended from the middle of the wire depresses the wire to shape ACB as shown in the figure. For the following figure, assume d<<L. ![Figure showing a wire of length 2L and radius r fixed at points A and B with a mass M suspended from the middle of the wire. The wire is deflected downwards to form a curve ACB.] (i) The increase in the length of the wire is: (a) d²/2L (b) d²/L (c) d²/L (d) d²/2L (ii) The strain in the wire is: (a) d/L (b) d/2L (c) 2d/L (d) d/2L (iii) The tension T in the wire is: (a) MgL/d (b) MgL/2d (c) 2MgL/d (d) MgL/4d (iv) The stress developed in the wire is: (a) MgL/πr²d (b) MgL/2πr²d (c) 2MgL/πr²d (d) MgL/4πr²d (v) The depression d at the midpoint of the wire is: (a) (L Mg / π²r²Y)^1/3 (b) (LMg / π²r²Y)^1/3 (c) (Mg / π²r²YL)^1/3 (d) (2L Mg / π²r²Y)^1/3 ## Section-E 18. Derive Bernoulli's equation for a streamline flow of an ideal fluid in a pipe. Use it to derive Torricell's law for speed of efflux from an open tank. **OR** Derive an expression for the height upto which a liquid will rise in a capillary. What will happen if the length of the capillary tube is less than the height to which the liquid will rise. 19. Prove that the motion of a simple pendulum is simple harmonic for small values of angular displacement θ. Hence derive an expression for its time period. What is the length of a simple pendulum, which ticks seconds? **OR** Explain formation of standing waves on a string fixed at one end. How nodes and antinodes are formed? Find the position of nodes and antinodes. What is the distance between node and its nearest antinode?