CBSE Class XI Physics Prep
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CBSE Class XI Physics Prep
English 31 leveled MCQs Free
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5 marks Long answer
(a) State and prove the law of conservation of mechanical energy for a freely falling body. (b) A body of 2 kg drops from 10 m. Find KE and PE at a height of 4 m. (g = 10 m/s²)
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Total energy conserved; KE = 80 J, PE = 40 J.
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5 marks Long answer
(a) Derive the relation v = ω × r. (b) A flywheel rotating at 1200 rpm decelerates uniformly at 2 rad/s². Find the number of rotations before it stops.
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v = ωr; Rotations = 120.
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5 marks Long answer
(a) Distinguish between conservative and non-conservative forces with examples. (b) Show that work done by a conservative force around a closed loop is zero. (c) Find PE stored in a spring (k=800 N/m) compressed by 5 cm.
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Conservative forces: path-independent; W = 0; PE = 10 J.
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5 marks Long answer
(a) Derive expressions for Time of flight, Max height, and Horizontal range of a horizontal projectile. (b) An aircraft flying horizontally at 490 m high with 180 km/h drops a package. Find the horizontal distance where it lands.
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Derive formulas; Distance = 1800 m.
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5 marks Long answer
Case Study 1: Friction in Daily Life. 1. Why is it easier to pull a lawn roller than to push it? (2 Marks) 2. A mass of 10 kg is on a rough surface (μs=0.5). A force of 40 N is applied. Find the frictional force. (2 Marks)
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Pulling reduces normal force, friction is less; Frictional force = 50 N.
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5 marks Long answer
Case Study 2: Elastic Collisions. 1. Derive the final velocities v1 and v2 after head-on elastic collision with a stationary mass. (2 Marks) 2. If a heavy mass hits a light stationary body, what are the final velocities? (2 Marks)
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v1 = (m1 - m2)/(m1 + m2)u; v2 = (2m1)/(m1 + m2)u.
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5 marks Long answer
(a) Explain the resolution of vectors in a 2D Cartesian plane. (b) Find the angle between vectors A = 2i + 2j - k and B = 6i - 3j + 2k using dot product.
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Resolution uses components; Angle = 60°.
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3 marks Medium answer
If a known standard length of 3.52 cm is measured by two instruments as 3.4 cm and 3.512 cm, identify which measurement is more precise and which is more accurate.
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3.512 cm is more accurate; 3.512 cm is more precise.
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3 marks Medium answer
Sketch the position-time (x-t) graph for an object moving with (i) positive uniform velocity, and (ii) negative acceleration.
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Graph shows a straight line for uniform velocity and a downward curve for negative acceleration.
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3 marks Medium answer
Two masses 5 kg and 10 kg are connected at the two ends of a light inextensible string passing over a frictionless pulley. Find the acceleration of the system when released. (g = 10 m/s2)
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Acceleration = 3.33 m/s².
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3 marks Medium answer
State the work-energy theorem for a variable force. Write its mathematical expression in integral form.
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Work done = ∫ F dx.
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3 marks Medium answer
Find the torque of a force F = -3i + j + 5k acting at the point r = 7i + 3j + k about the origin.
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Torque = (−3i + j + 5k) × (7i + 3j + k).
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3 marks Medium answer
Check the correctness of the relation n = (1/2L) * √(T/m) using dimensional analysis, where n is frequency, L is length, T is tension, and m is mass per unit length.
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Dimensions match, relation is correct.
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3 marks Medium answer
Derive the equations of motion v = u + at and s = ut + (1/2)at² using calculus methods.
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Use calculus to integrate acceleration to derive equations.
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3 marks Medium answer
Prove that the path followed by a projectile projected at an angle q with the horizontal is parabolic.
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Use parametric equations of motion to show parabolic path.
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3 marks Medium answer
Derive an expression for the optimum safe speed of a vehicle on a banked circular smooth track of radius r and angle θ.
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Optimum speed = √(rg tan θ).
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3 marks Medium answer
A pump fills a tank of 30 m³ in 15 minutes. The tank is 40 m high. If efficiency is 30%, find electric power consumed. (g=10 m/s²)
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Power = 300 W.
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3 marks Medium answer
State and prove the law of conservation of linear momentum using Newton's third law of motion.
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Momentum before = Momentum after; proven using collisions.
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3 marks Medium answer
Define radius of gyration. Derive the expression for the moment of inertia of a thin uniform circular ring of mass M and radius R about a tangent perpendicular to its plane.
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Radius of gyration k = √(I/M); I = MR².
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1 marks Short answer
The dimensional formula for absolute permittivity (e0) is:
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[M-1L-3T4A2]
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1 marks Short answer
A student measures the period of oscillation of a simple pendulum. In successive measurements, the readings are 2.63s, 2.56s, 2.42s, 2.71s, and 2.80s. The percentage error in the measurement is closest to:
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4%
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1 marks Short answer
A particle moves along a straight line such that its displacement x at time t is given by x = t3 - 6t2 + 3t + 4. The velocity of the particle when its acceleration becomes zero is:
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0 m/s
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1 marks Short answer
A bullet fired at an angle of 30° with the horizontal hits the ground 3 km away. By adjusting its angle of projection, keeping the velocity same, the maximum horizontal range achievable is:
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6 km
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1 marks Short answer
If the resultant of two vectors A and B is perpendicular to A and its magnitude is equal to half of the magnitude of B, then the angle between A and B is:
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120°
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1 marks Short answer
A block of mass 2 kg rests on a rough horizontal plane whose coefficient of static friction is 0.4. If a horizontal force of 2.5 N is applied to the block, the frictional force acting on the block will be: (Take g = 10 m/s2)
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2.5 N
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1 marks Short answer
A monkey of mass 40 kg climbs on a rope which can stand a maximum tension of 600 N. In which of the following cases will the rope break? (Take g = 10 m/s2)
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climbs up with an acceleration of 6 m/s2
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1 marks Short answer
The potential energy function for a particle executing linear simple harmonic motion is given by V(x) = kx2/2. If the total energy of the particle is E, then its speed at maximum displacement (x = xmax) is:
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Zero
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1 marks Short answer
A body of mass 0.5 kg travels in a straight line with velocity v = ax3/2 where a = 5 m-1/2s-1. The work done by the net force during its displacement from x = 0 to x = 2 m is:
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25 J
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1 marks Short answer
A solid cylinder of mass 2 kg and radius 0.2 m is rotating about its central axis at 40 rad/s. The rotational kinetic energy of the cylinder is:
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32 J
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1 marks Short answer
The position vector of the centre of mass of a system of two particles of masses 1 kg and 2 kg located at positions (1,2,1) and (-1,3,-1) respectively is:
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(-1/3, 8/3, -1/3)
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1 marks Short answer
When a net external torque acting on a system becomes zero, which of the following quantities remains strictly conserved?
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Angular Momentum
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