A body of mass $5\, kg$ is moving in a circle of radius $1\,m$ with an angular velocity of $2$ radian/sec. The centripetal force is ......... $N$
$10 $
$20$
$30 $
$40$
A hemispherical bowl of radius $R$ is rotated about its axis of symmetry which is kept vertical with angular velocity $\omega $ . A small block is kept in the bowl. It remains stationary relative to the bowl surface at a position where the radius makes an angle $\theta $ with the vertical. The friction is absent. The value of $\theta $ is
If the radius of curvature of the path of two particles of same mass are in the ratio $3:4,$ then in order to have constant centripetal force, their velocities will be in the ratio of:
Radius of the curved road on national highway is $R$. Width of the road is $b$. The outer edge of the road is raised by $h$ with respect to inner edge so that a car with velocity $v$ can pass safe over it. The value of $h$ is
A ball of mass $0.1\, Kg$. is whirled in a horizontal circle of radius $1\, m$. by means of a string at an initial speed of $10\, R.P.M.$ Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is ....... $r.p.m.$
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 $1.5\ m$ )