A particle of mass $m$ is executing uniform circular motion on a path of radius $r$. If $p$ is the magnitude of its linear momentum. The radial force acting on the particle is

A stone of mass of $16\, kg$ is attached to a string $144 \,m$ long and is whirled in a horizontal circle. The maximum tension the string can withstand is $16$ Newton. The maximum velocity of revolution that can be given to the stone without breaking it, will be ....... $ms^{-1}$

A particle is moving in a circle of radius $R$ with constant speed $v$, if radius is double then its centripetal force to keep the same speed should be

A plank is resting on a horizontal ground in the northern hemisphere of the earth at a $45^{\circ}$ latitude. Let the angular speed of the earth be $\omega$ and its radius $r_e$. The magnitude of the frictional force on the plank will be

A cyclist turns around a curve at $15\, miles/hour$. If he turns at double the speed, the tendency to overturn is

For a vehicle moving on a banked curved road, using free body diagram $(FBD)$, obtain the formula for the maximum safe speed $(v_{max})$.