If the radii of circular path of two particles of same mass are in the ratio of $1: 2$, then to have a constant centripetal force, the ratio of their speeds should be

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

The angular speed of a particle moving in a circular path is doubled. Then, the centripetal acceleration of the particle is

A spherical bob of mass 250 g is attached to the end of a string having length 50 cm . The bob is rotated on a horizontal circular path about a vertical axis. The maximum tension that the string can bear is 72 N . The maximum possible value of angular velocity of bob (in $\mathrm{rad} / \mathrm{s}$ ) is