$A$ body is moving on a circle of radius $80 \, m$ with a speed $20 \, m/s$ which is decreasing at the rate of $5 \, m/s^2$ at an instant. The angle made by its acceleration with its velocity is .......... (in $^{\circ}$)

$A$ particle at rest starts moving with a constant angular acceleration of $4 \ rad/s^2$ in a circular path. At what time will the magnitudes of its tangential acceleration and centrifugal acceleration be equal (in $s$)?

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

$A$ 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.

$A$ 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 $m/s^2$?

In a circular motion of a particle,the tangential acceleration of the particle is given by $a_t = 12 \ m/s^2$. The radius of the circle is $3 \ m$. The particle was initially at rest. The time after which the total acceleration of the particle makes an angle $45^{\circ}$ with the radial acceleration is