A point $P$ moves in 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 metres and $t$ is in seconds. The radius of the path is $20\ m$. The acceleration of '$P$' when $t = 2\ s$ is nearly ..........  $m/s^2$

What happens to the centripetal acceleration of a revolving body if you double the orbital speed $v$ and half the angular velocity $\omega $

An electron is moving in a circle of radius $2 \,m$ with speed $4 \,m / s$ Find the acceleration of the electron. (in $m / s ^{2}$)

Read each statement below carefully and state, with reasons, if it is true or false :

$(a)$ The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre

$(b)$ The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point

$(c)$ The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector

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

An athlete completes one round of a circular track of radius $10\, m$ in $40\, sec$. The distance covered by him in $2 \,min$ $20 \,sec$ is ........ $m$