The magnitude of the centripetal force acting on a body of mass $m$ executing uniform motion in a circle of radius $r$ with speed $v$ is

A particle of mass $M$ moves with constant speed along a circular path of radius $ r$ under the action of a force $F$. Its speed is

A cyclist goes round a circular path of circumference $34.3\, m$ in $\sqrt {22} $ sec. the angle made by him, with the vertical, will be ....... $^o$

The maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius $R$ and coefficient of static friction $\mu $, is

A car is negotiating a curved road of radius $R$. The road is banked at an angle $\theta .$ The coefficient of friction between the tyres of the car and the road is $\mu _s.$ The maximum safe velocity on this road is

A circular road of radius $1000 \,m$ has banking angle ${45^o}$. The maximum safe speed of a car having mass $2000 \,kg$ will be, if the coefficient of friction between tyre and road is $0.5$ ....... $m/s$