The kinetic energy $k$ of a particle moving along a circle of radius $R$ depends on the distance covered $s$ as $k = as^2$ where $a$ is a constant. The force acting on the particle is
$2a\frac{{{s^2}}}{R}$
$2as{\left( {1 + \frac{{{s^2}}}{{{R^2}}}} \right)^{1/2}}$
$2as$
$2a\frac{{{R^2}}}{s}$
A particle is moving in $x y$-plane in a circular path with centre at origin. If at an instant the position of particle is given by $\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$, then velocity of particle is along .......
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 .......... $rad / s ^2$
If $\theta$ is angle between the velocity and acceleration of a particle moving on a circular path with decreasing speed, then .........
A particle is tied to $20\, cm$ long string. It performs circular motion in vertical plane. What is the angular speed of particle when the tension in the string at the top is zero ......... $rad/sec$
A small block slides down from rest at point $A$ on the surface of a smooth cylinder, as shown. At point $B$, the block falls off (leaves) the cylinder. The equation relating the angles $\theta_1$ and $\theta_2$ is given by