Exercise (Previous Year Questions)

Four identical thin rods, each of mass $M$ and length $l$, form a square frame. The moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is,

If $\overrightarrow{F}$ be a force acting on a particle having the position vector $\overrightarrow{r}$ and $\overrightarrow{\tau }$ be the torque of this force about the origin. Then

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along,

If a solid cylinder of mass $3 \mathrm{kg}$ is rolling on a horizontal surface with velocity $4 \mathrm{m}/\mathrm{s}$. It collides with a horizontal spring of force constant $200 \mathrm{N}/\mathrm{m}$. The maximum compression produced in the spring will be

A solid cylinder of mass$50 kg$  and radius $0.5 m$ is free to rotate about a 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 $2 rev/s^2$ is 

From a disc of radius $R$ and mass $M$, a circular hole of diameter $R$, whose rim passes through the centre of the disc is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through the centre of the disc?

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ${\omega }_1$ and ${\omega }_2$. They are brought in to contact face to face coinciding the axis of rotation. The expression for the loss of energy during this process is:Enable GingerCannot connect to Ginger Check your internet connection
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A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?