A railway line is taken round a circular arc of radius $1000\ m$ , and is banked by raising the outer rail $h$ $m$ above the inner rail. If the lateral force on the inner rail when a train travels round the curve at $10\ ms^{-1}$ is equal to the lateral force on the outer rail when the train's speed is $20\ ms^{-1}$ . The value of $4g\ tan\theta $ is equal to : (The distance between the rails is $1.5\ m$ )

$A$ particle is moving in a circle :

For uniform circular motion write equation of centripetal force, centripetal acceleration. Also write examples.

Write equation of centripetal acceleration and centripetal force for uniform circular motion.

An unbanked curve has a radius of $60\,m$. The maximum speed at which a car can make a turn if the coefficient of static friction is $0.75$, is ...... $m/s$

A point mass $m$ is suspended from a light thread of length $l$, fixed at $O$, is whirled in a horizontal circle at constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are