A body is rolling down an inclined plane. If kinetic energy of rotation is $40\%$ of  translational kinetic energy, then the body is a

A thin rod of length $L$ and mass $M$ is held vertically with one end on the floor and is allowed to fall. Find the velocity of the other end when it hits the floor, assuming that the end on the floor does not slip

A rolling wheel of $12 \,kg$ is on an inclined plane at position $P$ and connected to a mass of $3 \,kg$ through a string of fixed length and pulley as shown in figure. Consider $PR$ as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom $Q$ of the inclined plane $P Q$ will be $\frac{1}{2} \sqrt{ xgh } \,m / s$. The value of $x$ is.............

A circular disc of mass $M$ and radius $R$ is rotating about its axis with angular speed $\omega_{1}$ If another stationary disc having radius $\frac{ R }{2}$ and same mass $M$ is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed $\omega_{2}$. The energy lost in the process is $p \%$ of the initial energy. Value of $p$ is

Two point masses of $0.3\ kg$ and $0.7\ kg$ are fixed at the ends of a rod of length $1.4\ m$  and of negligible mass. The rod is set rotating about an axis perpendicular  to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of  

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{sph}$ and $h_{cyl}$ on the incline. The radio $\frac{{{h_{sph}}}}{{{h_{cyl}}}}$ is given by