$A$ child of mass $5\,kg$ is going round a merry-go-round that makes $1$ rotation in $3.14\,s$. The radius of the merry-go-round is $2\,m$. The centrifugal force on the child will be $.......\,N$.

Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius of $(r/3)$ and the lighter one in a radius of $r$. The tangential speed of the lighter stone is $n$ times that of the heavier stone when they experience the same centripetal force. The value of $n$ is:

$A$ car moving at a speed of $72 \; km/hr$ passes through a point $P$ on a curved road with a radius of $10 \; m$. The mass of the car is $500 \; kg$. Find the contact force (normal force) at point $P$ in $kN$. (Take $g = 10 \; m/s^2$)

$A$ cyclist riding a bicycle at a speed of $14\sqrt{3} \text{ m/s}$ takes a turn around a circular road of radius $20\sqrt{3} \text{ m}$ without skidding. Given $g = 9.8 \text{ m/s}^2$,what is his inclination to the vertical in degrees?

$A$ stone of mass $16 \, kg$ is attached to a string $144 \, m$ long and is whirled in a horizontal circle. The maximum tension the string can withstand is $16 \, N$. The maximum velocity of revolution that can be given to the stone without breaking it will be ....... $m/s$.

$A$ ball of mass $m$ is attached to the free end of an inextensible string of length $\ell$. Let $T$ be the tension in the string. The ball is moving in a horizontal circular path about the vertical axis. The angular velocity of the ball at any particular instant will be