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 man is running with constant speed along a circular path of radius $2 \sqrt 2\, m$. He completes $1$ round in $10\, second$. Find instantaneous speed at $2.5 \,sec.$

Three particle $A, B$ and $C$ move in a circle of radius $r = \frac{1}{\pi }\,m$, in anticlockwise direction with speeds $1\, m/s$, $2. 5\, m/s$ and $2\, m/s$ respectively. The initial positions of $A, B$ and $C$ are as shown in figure. The ratio of distance travelled by $B$ and $C$ by the instant $A, B$ and $C$ meet for the first time is

If speed of a particle moving in a circle of radius $2\,m$ is given as $v = 2t + 2$, then its centripetal acceleration after $1\, s$ will be   ......... $m/s^2$

particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\vec a\, = \,(4\hat i + 3\hat j)\,\,m/{s^2}$ and $\vec P\, = \,(8\hat i\, - \,6\hat j)\,kg\, - \,m/s$ . The motion of the particle is

The centripetal acceleration is given by