$A$ uniform circular disc of radius $50\, cm$ at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of $2.0\, rad \,s^{-2}$. Its net acceleration in $m\,s^{-2}$ at the end of $2.0\,s$ is approximately (in $.0$)

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 $........ \text{ m}$.

$A$ 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 on a circular path with decreasing speed. Identify the correct statement.

$A$ train is moving at a speed of $50\, m s^{-1}$ on a curved track of radius $250\, m$. What is its acceleration (in $, m s^{-2}$)?

$A$ car moves with a speed of $30 \, m/s$ on a circular path of radius $500 \, m$. If its tangential acceleration is $2 \, m/s^2$,what is the magnitude of the total acceleration of the car in $m/s^2$?