$A$ particle moves in a circular path of radius $r$ with speed $v.$ It then increases its speed to $2v$ while travelling along the same circular path. The centripetal acceleration of the particle has changed by a factor of

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

In the given figure,$a = 15 \, m s^{-2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R = 2.5 \, m$ at a given instant of time. The speed of the particle is ........ $m/s$.

The acceleration of a body in a non-uniform circular motion is $5\, ms^{-2}$. Which one of the following is correct?

For a particle in circular motion,$a_r = 3 \ m/s^2$ and $a_T = 4 \ m/s^2$. If $\theta$ is the angle between the resultant acceleration $a$ and the radial acceleration $a_r$,then .......

$A$ car is travelling with linear velocity '$V$' on a circular road of radius '$r$'. If its velocity is increasing at a rate of '$a$' $ms^{-2}$, then the resultant acceleration will be