## MCQ (More than One Correct Answer)

A student skates up a ramp that makes an angle 30$$^\circ$$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with...

A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has n...

A particle of mass $$m$$ is initially at rest at the origin. It is subjected to a force and starts moving along the $$x$$-axis. Its kinetic energy $$K...

A flat plate is moving normal to its plane through a gas under the reaction of a constant force $$F.$$ The gas is kept at a very low pressure. The spe...

A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with veloc...

A force $$F = - K\left( {y\widehat i + x\widehat j} \right)$$ (where K is a positive constant) acts on a particle moving in the xy plane. Starting fr...

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the center. At a certain instant of time, the...

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle t...

A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. I...

A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in the time t is proportional to

## Numerical

A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force $$F = (\alpha y\widehat i + 2\alpha x\widehat j)$$ N, w...

A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $$2.0\,N{m^{ - 1}}$$ and the mass of the block...

Consider an elliptically shaped rail PQ in the vertical plane with
OP = 3 m and OQ = 4 m. A block of mass 1 kg is pulled along the
rail from P to Q wi...

A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to
the particle. If the initial speed (in m/s)...

A bob of mass m, suspended by a string of length l1 is given a minimum velocity required to complete a full circle in the vertical plane. At the highe...

A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The
coefficient of friction between the block and the floor is 0.1. Initially...

## MCQ (Single Correct Answer)

In the List-$${\rm I}$$ below, four different paths of a particle are given as functions of time. In these functions, $$\alpha $$ and $$\beta $$ are ...

A particle of unit mass is moving along the x-axis under the
influence of a force and its total energy is conserved. Four
possible forms of the potent...

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball dur...

The speed of the block when it reaches the point Q is

The magnitude of the normal reaction that acts on the block at the point Q is

The work done on a particle of mass m by a force
$$$K\left[ {{x \over {{{\left( {{x^2} + {y^2}} \right)}^{3/2}}}}\widehat i + {y \over {{{\left( {{x^2...

A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards, it is subjected to a time-dependent force F(t) in the x-d...

A piece of wire is bent in the shape of a parabola y = kx2 (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without frict...

A particle is acted by a force F = kx, where k is a +ve constant. Its potential energy at x = 0 is zero. Which
curve correctly represents the variatio...

If W1, W2 and W3 represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the
gravit...

An ideal spring with spring-constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spri...

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercept...

A spring of force-constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force-const...

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration $${a_c}$$ is varying with time t as $${a...

Two masses of 1gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is

If a machine is lubricated with oil