B M Sharma Solutions for Chapter: Center of Mass, Exercise 2: DPP 1.2

A system of two blocks $A$ and $B$ and a wedge $C$ is released from rest as shown in the figure. The masses of the blocks and the wedge are $m, 2m$ and $2m$, respectively. The displacement of wedge $C$ when block $B$ slides down the plane a distance $10 \mathrm{cm}$ is (neglect friction),

Two men $\mathrm{A}$ and $\mathrm{B}$ are standing on a plank. $\mathrm{B}$ is at the middle of the plank and $\mathrm{A}$ is at the left end of the plank. The system is initially at rest and masses are as shown in the figure. $\mathrm{A}$ and $\mathrm{B}$ start moving such that the position of $\mathrm{B}$ remains fixed with respect to ground, then $\mathrm{A}$ meets $\mathrm{B}$. Then, the point where $\mathrm{A}$ meets $\mathrm{B}$ is located at,

In the figure shown, the system is at rest, initially. Two persons, $A$ and $B$, of masses $40 \mathrm{kg}$ each, move with speeds $v_1$ and $v_2$, respectively, towards each other on a plank lying on a smooth horizontal surface as shown in the figure. The plank travels a distance of $20 \mathrm{m}$ towards right direction in $5 \mathrm{s}$. (Here, $v_1$ and $v_2$ are given with respect to the plank). Then,

$\left(\mathrm{i}\right)$ $v_1=10 \mathrm{m} {\mathrm{s}}^{-1}, v_2=0 \mathrm{m} {\mathrm{s}}^{-1}$

$\left(\mathrm{ii}\right)$ $v_1=15 \mathrm{m} {\mathrm{s}}^{-1}, v_2=5 \mathrm{m} {\mathrm{s}}^{-1}$

$\left(\mathrm{iii}\right)$ $v_1=20 \mathrm{m} {\mathrm{s}}^{-1}, v_2=10 \mathrm{m} {\mathrm{s}}^{-1}$

A small sphere of radius $R$ is held against the inner surface of a smooth spherical shell of radius $6R$ as shown in the figure. The masses of the shell and the small sphere are $4M$ and $M$, respectively.

This arrangement is placed on a smooth horizontal table. The small sphere is now released. The $x$-coordinate of the center of the shell when the smaller sphere reaches the other extreme position is,

Two balls of same mass are released simultaneously from heights $h$ and $2h$ from the ground level. The balls collide with the floor and stick to it. The velocity-time graph of center of mass of the two balls is best represented by,

Two particles of equal mass $m$ are projected from the ground with speeds $v_1$ and $v_2$ at angles ${\theta }_1$ as ${\theta }_2$ shown in the figure.

Which of the following are correct?

Two identical rods are joined at one of their ends by a pin. The joint is smooth and rods are free to rotate about the joint. The rods are released in vertical plane on a smooth surface as shown in the figure. The displacement of the joint from its initial position to the final position is (i.e., when the rods lie straight on the ground),