D. C. Pandey Solutions for Chapter: Rotation, Exercise 1: Objective Problems

A rod of length $L$ whose lower end is fixed along the horizontal plane starts to topple from the vertical position. The velocity of the upper end of the rod when it hits the ground is

A ring starts to roll down the inclined plane of height $h$ without slipping. The velocity with which it reaches the ground is

The angular momentum of a particle describing uniform circular motion is $L$. If its kinetic energy is halved and angular velocity doubled, its new angular momentum is

A solid sphere of mass $m$ rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is $v$. The kinetic energy of the sphere at the bottom is

A binary star consists of two stars, $A$ $\left(\mathrm{mass} 2.2 {\mathrm{M}}_{\mathrm{S}}\right)$ and $B$ $\left(\mathrm{mass} 11 {\mathrm{M}}_{\mathrm{S}}\right),$ where $M_{\mathrm{S}}$ is the mass of the sun. They are separated by distance $d$ and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of the star $B$ about the centre of mass is

From a circular ring of mass $M$ and radius $R\text{,}$ an arc corresponding to a $90°$ sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is $k$ times $M{R}^2\text{.}$ Then, the value of $k$ is

A wheel of moment of inertia $2.5 \mathrm{kg} {\mathrm{m}}^2$ has an initial angular velocity of $40 \mathrm{rad} {\mathrm{s}}^{-1}\text{.}$ A constant torque of $10 \mathrm{N} \mathrm{m}$ acts on the wheel. The time during which the wheel is accelerated to $60 \mathrm{rad} {\mathrm{s}}^{-1}$ is

Which relation is not correct of the following?