A disc of mass $M$ and radius $R$ rolls in a horizontal surface and then rolls up an inclined plane as shown in the fig. If the velocity of the disc is $v$, the height to which the disc will rise will be..
$\frac{{3{v^2}}}{{2g}}$
$\frac{{3{v^2}}}{{4g}}$
$\frac{{{v^2}}}{{4g}}$
$\frac{{{v^2}}}{{2g}}$
The total kinetic energy of a body of mass $10\ kg$ and radius $0.5\ m$ moving with a velocity of $2\ m/s$ without slipping is $32.8\ joule$. The radius of gyration of the body is .......... $m$
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 square plate is spun around different axes with the same angular speed. In which of the following choice of axis of rotation will the kinetic energy of the plate be the largest?
A thin uniform rod oflength $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end . Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of:
A disc is rolling without slipping on a straight surface. The ratio of its translational kinetic energy to its total kinetic energy is