K K Sharma Solutions for Chapter: Circular Motion, Exercise 1: TOPICWISE QUESTIONS

A block of mass $m$ slides down along the surface of the bowl from the rim to the bottom as shown in the figure. The velocity of the block at the bottom will be

A mass $m$ is revolving in a vertical circle at the end of a string of length $20 \mathrm{cm}$. By how much does the tension of the string at the lowest point exceed the tension at the topmost point? (Assume that the mass $m$ has speed at its lowest point such that it is just able to complete the vertical circle)

A particle initially at rest starts moving from point $A$ on the surface of a fixed smooth hemisphere of radius $r$, as shown. The particle loses its contact with the hemisphere at point $B$. $C$ is the centre of the hemisphere. The equation relating $\alpha$ and $\beta$ is

A block follows the path as shown in the figure, from height $h.$ If radius of the circular path is $r,$ then the relation which holds good to complete the full circle is

A particle of mass $m$, attached to the end of a string of length $l$, is released from the initial position $A$, as shown in the figure. The particle moves in a vertical circular path $O.$ When it is vertically below $O,$ the string makes contact with nail $N$ placed directly below $O$ at a distance $h$ and rotates around it. If the particle just completes the vertical circle about $N,$ then 

A particle suspended from a fixed point by a light inextensible thread of length $l$, is projected horizontally from its lowest position with velocity $\sqrt{\frac{7gl}{2}}$. The thread will slack after swinging through an angle $\alpha$, such that $\alpha$ equals

A particle is kept at rest at the top of a sphere of diameter $42 \mathrm{cm}$. When disturbed slightly, it slides down. At what height $h$ from the bottom, will the particle leave the sphere?

A small block slides with velocity $0.5\sqrt{gr}$ on a horizontal frictionless surface, as shown in the figure. The block leaves the surface at point $C$. The angle $\theta$ in the figure is: