B M Sharma Solutions for Chapter: Rigid Body Dynamics I, Exercise 1: DPP 2.1

A $0.6 \mathrm{m}$ radius drum carrying the load $A$ is rigidly attached to a $0.9 \mathrm{m}$ radius pulley carrying the load $B$ as shown. At the time $t=0$, the load $B$ moves with a velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$ (downward) and a constant acceleration of $3 \mathrm{m} {\mathrm{s}}^{-2}$ (downward). Over the time interval, $0\le t\le 2 \mathrm{s}$, determine:

(i) the number of revolutions executed by the pulley.
(ii) the displacement of the load $A$.

Two points of a rod move with velocities $3v$ and $v$, perpendicular to the rod and in the same direction, separated by a distance $r$. Then, the angular velocity of the rod is

Two steel balls of equal diameter are connected by a rigid bar of negligible weight, as shown, and are dropped in the horizontal position from height $h$ above the heavy steel and brass base plates. If the coefficient of restitution between the ball and steel base is $0.6$ and that between the other ball and the brass base is $0.4$, the angular velocity of the bar immediately after rebound is,

(Assume the two impacts are simultaneous and take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Two points $\mathrm{A}$ and $\mathrm{B}$ on a disc have velocities $v_1$ and $v_2$, at some moment. Their directions make angles $60°$ and $30°$, respectively with the line of separation, as shown in the figure. The angular velocity of disc is:

When a person throws a meter stick, it is found that the centre of the stick is moving with a speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$ and left end of stick, with a speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$. Both points move vertically upwards at that moment. Then angular speed of the stick is

A ring of radius $R$ rolls without slipping on a rough horizontal surface with a constant velocity. The radius of curvature of the path followed by any particle of the ring at the highest point of its path will be:

A rigid body is in pure rotation, that is, undergoing fixed axis rotation. Then, which of the following statement(s) are true.

A particle is revolving in a circle of radius $r$, having centre at $\mathrm{O}$, with uniform angular velocity$\omega .$

Choose the correct option(s):