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 ....... $^o$

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 ......... $m/s$

A ball is released from rest from point $P$ of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point $Q$ is $A$ while angular position of point $Q$ is $\alpha$ with respect to point $P$. Which of the following graphs represent the correct relation between $A$ and $\alpha$ when ball goes from $Q$ to $R$ ?

How centripetal is provided while taking turn on level circular track ?

A body of mass $'m '$ is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is $1\, cm$. If the angular velocity is doubled, the elongation in the spring is $5\, cm$. The original length of the spring is .........  $cm$

A block of $200\, g$ mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius $20\, cm$. If the block takes $40\, s$ to complete one round, the normal force by the side walls of the groove is