$A$ particle of mass $m$ is rotating in a plane in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on the particle is

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

One end of a massless spring of spring constant $k$ and natural length $l_{0}$ is fixed,while the other end is connected to a small object of mass $m$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing through the fixed end,then the elongation of the spring will be

$A$ coin placed on a rotating turntable just slips if it is placed at a distance of $4 \ cm$ from the centre. If the angular velocity of the turntable is doubled,it will just slip at a distance of: (in $cm$)

If mass,speed,and radius of the circular path of a particle are increased by $100 \%$,then the necessary force required to maintain the circular path will have to be increased by (in $\%$)

$A$ train is moving towards north. At one place it turns towards north-east,here we observe that