$A$ car is travelling at $30 \,ms^{-1}$ speed on a circular road of radius $300 \,m$. If its speed is increasing at the rate of $4 \,ms^{-2}$, then its acceleration is (in $\,ms^{-2}$)

$A$ 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 $.0$)

$A$ 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.

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

Explain the effects of the radial component and the tangential component of the linear acceleration of a particle in circular motion.

The acceleration of a train travelling with a speed of $400 \, m/s$ as it goes round a curve of radius $160 \, m$ is: