$A$ stone of mass $0.3\,kg$ attached to a $1.5\,m$ long string is whirled around in a horizontal circle at a speed of $6\,m s^{-1}$. The tension in the string is $............\,N$.

$A$ ball of mass $0.25 \,kg$ attached to the end of a string of length $1.96 \,m$ is moving in a horizontal circle. The string will break if the tension is more than $25 \,N$. What is the maximum speed with which the ball can be moved (in $\,m/s$)?

$A$ particle of mass $m$ is rotating in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on it is $F$. The relation between $F$,$L$,$r$,and $m$ is

$A$ train is moving with a speed of $12 \,m/s$ on rails which are $1.5 \,m$ apart. To negotiate a curve of radius $400 \,m$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g = 10 \,m/s^2$): (in $\,cm$)

Find the centripetal force acting on a coin weighing $0.1 \,kg$ placed $0.1 \,m$ from the centre on a gramophone disc rotating at $600 \,rpm$.

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