Previous year questions with solutions · 2000 – 2026
| Year | Questions | Papers | Avg / paper | Weightage |
|---|---|---|---|---|
| 2026 | 4 | 2 | 2 | 4.44% ▼ 33.3% vs last year |
| 2025 | 3 | 1 | 3 | 6.67% ▲ 122.2% vs last year |
| 2024 | 3 | 2 | 1.5 | 3.00% ▼ 25% vs last year |
| 2023 | 2 | 1 | 2 | 4.00% ▼ 20% vs last year |
| 2022 | 5 | 2 | 2.5 | 5.00% ▲ 25% vs last year |
| 2021 | 2 | 1 | 2 | 4.00% ▼ 10% vs last year |
| 2020 | 2 | 1 | 2 | 4.44% same as last year |
| 2019 | 2 | 1 | 2 | 4.44% ▼ 50% vs last year |
| 2018 | 4 | 1 | 4 | 8.89% ▲ 33.3% vs last year |
| 2017 | 3 | 1 | 3 | 6.67% same as last year |
| 2016 | 6 | 2 | 3 | 6.67% same as last year |
| 2015 | 6 | 2 | 3 | 6.67% ▲ 50% vs last year |
| 2014 | 2 | 1 | 2 | 4.44% same as last year |
| 2013 | 4 | 2 | 2 | 4.44% ▼ 49.2% vs last year |
| 2012 | 7 | 2 | 3.5 | 8.75% ▲ 130.4% vs last year |
| 2011 | 3 | 2 | 1.5 | 3.80% ▼ 48.7% vs last year |
| 2010 | 6 | 2 | 3 | 7.41% ▼ 9.3% vs last year |
| 2009 | 4 | 1 | 4 | 8.16% ▲ 91.8% vs last year |
| 2008 | 2 | 1 | 2 | 4.26% ▼ 33.3% vs last year |
| 2007 | 3 | 1 | 3 | 6.38% ▲ 59.6% vs last year |
| 2006 | 2 | 1 | 2 | 4.00% ▼ 37.3% vs last year |
| 2005 | 3 | 1 | 3 | 6.38% ▼ 41.3% vs last year |
| 2004 | 5 | 1 | 5 | 10.87% ▲ 88.4% vs last year |
| 2003 | 3 | 1 | 3 | 5.77% ▼ 45.8% vs last year |
| 2002 | 5 | 1 | 5 | 10.64% ▲ 421.3% vs last year |
| 2001 | 1 | 1 | 1 | 2.04% ▼ 54.1% vs last year |
| 2000 | 2 | 1 | 2 | 4.44% |
A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?
From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?
A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s-2. Its net acceleration in m s-2 at the end of 2.0 s is approximately
Two rotating bodies A and B of masses m and 2m with moments of inertia IA and IB (IB > IA) have equal kinetic energy of rotation. If LA and LB be their angular momenta respectively, then
A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (Esphere/Ecylinder) will be
A light rod of length l has two masses m1 and m2 attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is
Point masses m1 and m2 are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity 0 is minimum, is given by [figure]
An automobile moves on a road with a speed of 54 km h-1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m2. If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its brakes to the wheel is
A force F = i + 3 j + 6 k is acting at a point r = 2 i - 6 j - 12 k. The value of for which angular momentum about origin is conserved is
A rod of weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A. The normal reaction on A is
A mass m moves in a circle on a smooth horizontal plane with velocity v0 at a radius R0. The mass is attached to a string which passes through a smooth hole in the plane as shown. The tension in the string is increased gradually and finally m moves in a circle of radius R02. [figure] The final value of the kinetic energy is
Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX' axis is [figure]
A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s-2 is
The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle without slipping and slipping down the incline without rolling is
A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is [figure]
A small object of uniform density rolls up a curved surface with an initial velocity 'v'. It reaches upto a maximum height of 3v24g with respect to the initial position. The object is
The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are
Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1 has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s-1. Disc D2 has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s-1. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s-1) of the system is
A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m2. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 m s-1 relative to the ground. Time taken by the man to complete one revolution is
The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through [figure]
Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is :
A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s-1. It collides with a horizontal spring of force constant 200 N m-1. The maximum compression produced in the spring will be
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along
Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by:
ABC is an equilateral triangle with O as its centre. F1, F2 and F3 represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then magnitude of F3 is [figure]
A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will [figure]
The instantaneous angular position of a point on a rotating wheel is given by the equation (t) = 2t3 - 6t2 The torque on the wheel becomes zero at
The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
From a circular disc of radius R and mass 9M, a small disc of mass M and radius R3 is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is
A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?