$A$ particle of mass $5 \ kg$ is moving on a circle of radius $1 \ m$ with an angular velocity of $2 \ rad \ s^{-1}$. The centripetal force is (in $N$)

$A$ particle moves in a circular path of radius $r$ with speed $v.$ It then increases its speed to $2v$ while travelling along the same circular path. The centripetal acceleration of the particle has changed by a factor of

$A$ stone is tied to one end of a string $50\, cm$ long and is whirled in a horizontal circle with a constant speed. If the stone makes $10$ revolutions in $20\, s$,what is the magnitude of the acceleration of the stone in $cm/s^2$?

$A$ particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration is varying with time as $a_c = k^2rt^2$. The power delivered to the particle by the forces acting on it is $(k = \text{constant})$

$A$ disc is rotating with constant angular velocity $\omega$ about an axis passing through centre $C$ and perpendicular to the plane of the disc. An insect is moving over the disc along the radial direction with constant velocity $v$ with respect to the disc. The acceleration of the insect at the instant when its distance from the centre is $r$ will be :-

$A$ particle moves along a circle of radius $3 \, m$ with its displacement given by $S = \frac{t^2}{2} + \frac{t^3}{3}$. The total acceleration at $t = 2 \, s$ is ....... $m/s^2$.