$A$ particle is moving in a circle of radius $R$ with constant speed $v$. If the radius is doubled while keeping the speed the same,what happens to the centripetal force?

The magnitude of the centripetal force acting on a body of mass $m$ executing uniform circular motion in a circle of radius $r$ with speed $v$ is:

The velocity and acceleration vectors of a particle undergoing circular motion are $\overrightarrow{v} = 2 \hat{i} \text{ m/s}$ and $\overrightarrow{a} = 2 \hat{i} + 4 \hat{j} \text{ m/s}^2$ respectively at an instant of time. The radius of the circle is $........ \text{ m}$.

$A$ 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:

$A$ 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 .......... $m/s^2$.

$A$ particle of mass $m$ is moving in a circular path of constant radius $r$ such that its tangential acceleration varies with time as $a_t = K^2rt^2$ ($K$ is a constant). Select the correct statement.