If the angular velocity of a merry-go-round is $60^o/sec$ and you are $3.5\,m$ from the centre of rotation, your linear velocity will be

A sphere of diameter $r$ is cut from a sphere of radius $r$ such that the centre of mass of the remaining mass be at maximum distance from original centre; then the distance is

If the earth were to suddenly contract to $1/n^{th}$ of its present radius without any change in its mass, the duration (in $hrs.$ ) of the new day will be nearly

A uniform solid sphere of mass $m$ and radius $r$ rolls without slipping down a inclined plane, inclined at an angle $45^o$ to the horizontal. Find the magnitude of frictional coefficient at which slipping is absent

A particle of mass $= 5\ units$ is moving with a uniform speed $V = 3 \sqrt 2\ units$ in the $XOY$ Plane along the line $Y = X+4 $ . The magnitude of the angular momentum of the particle about the origin is ...... $unit.$

What is the moment of inhertia of a solid sphere of radius $R$ and density $\rho $ about its diameter ?