A body of mass $m$ slides down along a frictionless inclined plane from height $h$ and just completes motion in a vertical circle of radius 2 m after reaching the bottom. What is the value of $h$ ? [Use, $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

A merry-go-round rotating at a constant angular speed completes 9 rotations is 18 s . What is its angular speed?

Consider a particle is moving with a minimum speed $v$ at highest point of vertical circle of radius $R$. If the radius of the circle doubled the corresponding minimum speed will be

Assume proton is rotating along a circular path of radius 1 m under a centrifugal force of $4 \times 10^{-12} \mathrm{~N}$. If the mass of proton is $1.6 \times 10^{-27} \mathrm{~kg}$, then its angular velocity of rotation is