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:

$A$ particle moves in the $xy$-plane with velocity $\vec{v} = x \hat{i} + yt \hat{j}$. At $t = \frac{x \sqrt{3}}{y}$,the tangential and normal accelerations are:

If the radius of curvature of the path of two particles of same mass are in the ratio $3:4,$ then in order to have constant centripetal force,their velocities will be in the ratio of:

$A$ particle is moving in a circle of radius $50 \ cm$ in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at $t=0$ is $4 \ m/s$,the time taken to complete the first revolution will be $\frac{1}{\alpha}[1-e^{-2 \pi}] \ s$,where $\alpha=$ . . . . . . .

$A$ 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:

In non-uniform circular motion,the ratio of tangential to radial acceleration is ($r=$ radius,$\alpha=$ angular acceleration,$V=$ linear velocity).