The moment of inertia of a uniform rod of length $2l$ and mass $m$ about an axis $xy$ passing through its centre and inclined at an angle $\alpha$ is

A particle projected with velocity u at angle $\theta$ with horizontal at t=0. What is the magnitude of change in the velocity of the particle when it is at maximum height?

A ball strikes a wall with a velocity $\vec{u}$ at an angle $\theta$ with the normal to the wall surface. and rebounds from it at an angle $\beta$ with the surface. Then

Three identical spheres each of radius $R$ are placed thouching each other on a horizontal table as shown in figure. The co-ordinates of centre of mass are :
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A ball of mass 'm' moving with a horizontal velocity 'v' strikes the bob of mass 'm' of a pendulum at rest. During this collision, the ball sticks with the bob of the pendulum. The height to which the combined mass raises is (g = acceleration due to gravity).

A block slides down a rough inclined plane of slope angle $\theta$ with a constnat velocity. It is then projected up the same plane with an intial velocity v the distance travelled by the block up the plane coming to rest is .

A rod AB of length 2 m and mass 2 kg is lying on a smooth horizontal x-y plane with its centre at origin O as shown in figure. An impulse J of magnitude 10 N-s is applied perpendicular to AB at A.

Co-ordinates of point A of the rod after time t$=\frac{\pi }{45}$ s will be

A rigid mass less rod of length $L$ is hinged at its one end a weight $W$ is hung at a distance $l\left(<L\right)$ from this end.
What is force $P$ should be applied upwards at the other end so that the rod remains in equilibrium horizontally ?
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Pulling force making an angle $\theta$ to the horizontal is applied on a block of weight $W$ placed on a horizontal table. If the angle of friction is $\alpha$, then the magnitude of force is $\alpha$ , then the magnitude of force required to move the body is equal to

A small coin of mass $80g$ is placed on the horizontal surface of a rotating disc. The disc starts from rest and is given a constant angular acceleration $\alpha =2rad/s^2.$ The coefficient of static friction between the coin and the disc is ${\mu }_s=3/4$ and cofficient of kinetic friction is ${\mu }_k=0.5.$ The coin is placed at a distance $r=1m$ from the centre of the disc. The magnitude of the resultant force on the coin exerted by the disc just before it starts slipping on the disc is