$A$ particle moves in a circular path of radius $R$ with an angular velocity $\omega = a - bt$,where $a$ and $b$ are positive constants and $t$ is time. The magnitude of the acceleration of the particle after time $t = \frac{2a}{b}$ is:

$A$ point $P$ moves in a counter-clockwise direction on a circular path as shown in the figure. The movement of $P$ is such that it sweeps out a length $s = t^3 + 5$,where $s$ is in meters and $t$ is in seconds. The radius of the path is $20 \ m$. The acceleration of $P$ when $t = 2 \ s$ is nearly .......... $m/s^2$.

For a particle in circular motion,$a_r = 3 \ m/s^2$ and $a_T = 4 \ m/s^2$. If $\theta$ is the angle between the resultant acceleration $a$ and the radial acceleration $a_r$,then .......

$A$ particle is moving in a circular path of radius $r$ under the action of a force $F$. If at an instant the velocity of the particle is $\vec{v}$,and the speed of the particle is increasing,then:

The acceleration of a train travelling with a speed of $400 \, m/s$ as it goes round a curve of radius $160 \, m$ is:

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