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 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 ....... $^o$

A hemispherical bowl of radius $r$ is set rotating about its axis of symmetry in vertical. A small block kept in the bowl rotates with bowl without slipping on its surface. If the surface of the bowl is smooth and the angle made by the radius through the block with the vertical is $\theta$, then find the angular speed at which the ball is rotating.

Four identical point masses $'m'$ joined by light string of length $'l'$ arrange such that they form square frame. Centre of table is coincide with centre of arrangment. If arrangement rotate with constant angular velocity $'\omega '$ , find out tension in each string

Assuming the coefficient of friction between the road and tyres of a car to be $0.5$, the maximum speed with which the car can move round a curve of $40.0\, m$ radius without slipping, if the road is unbanked, should be ......... $m/s$

$Assertion$ : Mountain roads rarely go straight up the slope.
$Reason$ : Slope of mountains are large, therefore more chances of vehicle to slip from roads