West Bengal Wbchse Class 11 Physics — Real Previous-Year Papers

The displacement of a body of mass 3 kg under the action of a force is S = t²/3 metre. The work done in time 2s by the same force in (J) is (a) 2 (b) 3.8 (c) 5.2 (d) 2.66

Keeping the mass fixed, if the radius of the earth is halved, the acceleration due to gravity at any place will be (a) half of the original (b) one-fourth of the original (c) double of the original (d) four times of the original

The dimension of surface tension is (a) MLT⁻² (b) MLT⁻¹ (c) MT⁻² (d) ML²T⁻²

The speed of a ball of radius 2 cm in a viscous liquid medium is 20 cms⁻¹. The speed of a ball of radius 1 cm in the same liquid will be (a) 5 cms⁻¹ (b) 10 cms⁻¹ (c) 40 cms⁻¹ (d) 80 cms⁻¹

The perfect gas equation for 4 g of hydrogen gas is (a) PV = RT (b) PV = 2RT (c) PV = (1/2)RT (d) PV = 4RT

When 110 J of heat is supplied to a gaseous system, the internal energy of the system increases by 40 J. The amount of external work done (in J) is (a) 150 (b) 70 (c) 110 (d) 40

The path difference of two particles on a wave corresponding to a phase difference of 60° is (a) 2λ (b) λ/2 (c) λ/6 (d) λ/3

A particle executes a simple harmonic motion with frequency f. The frequency at which the kinetic energy of the particle changes is (a) f/2 (b) f (c) 2f (d) 4f

What are the significant figures in the result of addition of 9.8 and 15.298?

Which one of the kinematic equations states the work-energy principle? **OR** If A⃗ = 0.4î + 0.3ĵ + ck̂ be a unit vector, then what is the value of c?

When a copper sphere is heated, which physical quantity of the sphere will show maximum percentage change? **OR** Which two of the following physical quantities are dimensionally alike? (a) Surface tension (b) Pressure (c) Coefficient of viscosity (d) Coefficient of elasticity.

When sound enters water from air or vice-versa, which physical quantity of the waves remains unchanged?

Find the angle between the two vectors A⃗ = î - 2ĵ + 3k̂ and B⃗ = 2î + ĵ + 4k̂. **OR** The distance-time graph of a moving particle is given by x = 4t - 6t². i) What is the positive maximum speed? ii) At what time would the speed of the particle be zero? (x is in metre and t is in second)

A car of mass M moves upward with a constant speed v along an inclined road making an angle θ with the horizontal. If μ be the coefficient of friction between the road and the wheel of the car, show that the power of the engine of the car is P = vMg (sin θ + μ cos θ). **OR** A balloon at rest on the ground is rising upward with acceleration g/8. A stone is dropped from the balloon when it is at height H. Show that the time taken by the stone to touch the ground is 2√(H/g).

What is critical velocity (Vc)? Show that Vc = Nη/ρr, the terms have usual meanings. **OR** A spring having spring constant K is cut into two parts in the ratio 1 : 2. Find the spring constants of the two parts.

From the relation P = (1/3) mn C²rms, show that the mean kinetic energy of a molecule is the same for all types of gases. **OR** Write down the mathematical form of the first law of thermodynamics. Mention the different terms.

Two travelling waves superpose to form a stationary wave whose equation is y(x, t) = 5 sin(0.1πx) cos 50πt, where x, y are in cm and t is in sec. Find the equations of the two superposing travelling waves. **OR** Show that the equation x = a sin ωt + b cos ωt represents a simple harmonic motion.

Define coefficient of static friction. An object of weight W rests on an inclined plane. The coefficient of friction between the object and the plane is μ. For what value of the angle of inclination θ, will the object move downward with uniform speed under its own weight?

a) A balloon of mass m is descending with an acceleration α. What mass should be dropped from the balloon so that it starts moving upward with the same acceleration α? b) Define inertial frame of reference. **OR** Define centripetal force. A particle of mass m is rotating around a circular path of radius r. Find the centripetal acceleration of the particle and the magnitude and direction of the centripetal force acting on it.

A particle moves from a point r⃗₁ = î + 2ĵ in metre to another point r⃗₂ = 2î + 4ĵ in metre under the action of a force F⃗ = 2î + 3ĵ in newton. Find the work done by the force on the particle in the displacement. **OR** Define conservative force. Show that the work done around a closed path in a conservative force field is zero.

Define angular momentum (L⃗) and torque (τ⃗). Show that dL⃗/dt = τ⃗. **OR** A uniform solid sphere of mass M and radius R rolls down an inclined plane making an angle θ with the horizontal without slipping. Show that the acceleration of the sphere is (5/7)g sin θ. Given: moment of inertia of the sphere is (2/5)MR².

Define centre of mass. Write down its mathematical form. Two particles of masses 2g and 3g are situated at the positions (2 cm, 3 cm) and (4 cm, 5 cm) respectively. Find the position vector of the centre of mass of the two particles.

Define velocity of escape. Find an expression of the velocity of escape of a body projected from the surface of the earth. **OR** Show that the angular momentum of a planet is a conserved quantity. From the result obtain Kepler's second law.

Define acceleration due to gravity. Deduce an expression of the acceleration due to gravity at a place on the surface of the earth due to its rotation. **OR** What is meant by gravitational potential energy? Deduce an expression of the total energy of a planet in its orbit.

Define degrees of freedom. Write down the principle of equipartition of energy. Find the value of γ (= Cp/Cv) of a diatomic gas. **OR** Show that for ideal gas Cp - Cv = R and γ = 1 + 2/f, where f is the degrees of freedom of the molecule.

A quantity of an ideal gas is compressed from state (P₁, V₁) to another state (P₂, V₂) (i) isothermally, (ii) adiabatically. In which process will the work done be greater?

a) A particle is projected with an initial velocity u, making an angle θ with the horizontal. Find the equation of the trajectory of the particle at any instant after the projection. Find expressions for the maximum height gained by the particle and its horizontal range. b) What are the quantities that remain constant during the motion of the particle? **OR** a) What is meant by relative velocity? A particle A is moving with a velocity u. Another particle B is moving with a velocity v in a direction making an angle θ with the direction of motion of the first particle. Find an expression of the velocity of the second particle relative to the velocity of the first particle. b) Draw the velocity-time graph of a particle moving with non-uniform acceleration. From the graph find the instantaneous and average acceleration of the particle.

What are meant by turbulent flow and stream-line flow? Find the dimension of coefficient of viscosity. Write down Stokes' law and derive it from dimensional analysis.

Define simple harmonic motion. Find the expressions of the potential energy, kinetic energy and total energy of a particle performing a simple harmonic motion. Show their variations graphically. **OR** a) What are beats? Two tuning forks of frequencies f₁ and f₂ are vibrating in air medium. Find the frequency of the beat produced due to the superposition of the waves produced. b) Two tuning forks vibrating simultaneously produce 5 beats per sec. Frequency of one fork is 275 Hz. A small wax is attached to the other fork and 2 beats per sec are produced when the two vibrate simultaneously. Find the frequency of the other fork.