A motor cyclist has to rotate in horizontal circles inside the cylindrical wall of inner radius ' $R$ ' metre. If the coefficient of friction between the wall and the tyres is ' $\mu_{\mathrm{s}}$ ', then the minimum speed required is ( $\mathrm{g}=$ acceleration due to gravity)

The figure shows two masses ' $m$ ' and ' $M$ ' connected by a light string that passes through ${ }_a$ small hole ' $O$ ' at the centre of the table. Mass ' $m$ ' is moved round in a horizontal circle with ' $O$ ' as the centre. The frequency with which ' $m$ ' should be revolved so that ' $M$ ' remains stationary is

( $\mathrm{g}=$ gravitational acceleration)

Radius of curved road is ' $R$ ', width of road is ' $b$ '. The outer edge of road is raised by ' $h$ ' with respect to inner edge so that a car with velocity ' $V$ ' can pass safe over it, then value of ' $h$ ' is ( $\mathrm{g}=$ acceleration due to gravity)

Two bodies of mass 10 kg and 5 kg are moving in concentric circular orbits of radii ' R ' and ' r ' respectively such that their periods are same. The ratio between their centripetal acceleration is