If a cycle wheel of radius $4 \,m$ completes one revolution in two seconds. Then acceleration of a point on the cycle wheel will be
${\pi ^2}m/{s^2}$
$2{\pi ^2}m/{s^2}$
$4{\pi ^2}m/{s^2}$
$8\pi \,m/{s^2}$
A car is moving with a uniform speed on a level road. Inside the car there is a balloon filled with helium and attached to a piece of string tied to the floor. The string is observed to be vertical. The car now takes a left turn maintaining the speed on the level road. The balloon in the car will
A particle is revolving in a circular path of radius $25 \,m$ with constant angular speed $12 \,rev/min$. Then the angular acceleration of particle is .......... $rad / s ^2$
The work done on a particle of mass $m$ by a force, $k\left[\frac{x}{\left(x^2+y^2\right)^{3 / 2}} \hat{i}+\frac{y}{\left(x^2+y^2\right)^{3 / 2}} \hat{j}\right]$ ( $K$ being a constant of appropriate dimensions), when the particle is taken from the point $(a, 0)$ to the point $(0, a )$ along a circular path of radius a about the origin in the $x$-y plane is :
A particle starting from rest, moves in a circle of radius $r$. It attains a velocity of $\mathrm{V}_{0} \;\mathrm{m} / \mathrm{s}$ in the $\mathrm{n}^{\text {th }}$ round. Its angular acceleration will be
A particle comes round a circle of radius $1 \,m$ once. The time taken by it is $10 \,sec$. The average velocity of motion is