Exercise-3

A body of mass $(4 \mathrm{m})$ is lying in $\mathrm{x}-\mathrm{y}$. plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass $\left(\mathrm{m}\right)$ move perpendicular to each other with equal speeds $\left(\mathrm{v}\right)$. The total kinetic energy generated due to explosion is
 

A rigid ball of mass $\mathrm{m}$ strikes a rigid wall at $60°$ and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall in the ball will be 

Two identical balls $A$ and $B$ having velocities of $0.5 \mathrm{m} {\mathrm{s}}^{-1}$ and $-0.3 \mathrm{m} {\mathrm{s}}^{-1}$ respectively collide elastically in one dimension. The velocities of $B$ and $A$ after the collision respectively will be
 

Two small particles of equal masses start moving in opposite directions from a point $A$ in a horizontal circular orbit. Their tangential velocities fare $v$ and $2 v$, respectively, as shown in the figure. Between collisions, the particles move at constant speeds. After making how many elastic collisions, other than that at $A$, these two particles will again reach the point$A ?$

A ball of mass $0.2 \mathrm{kg}$ rests on a vertical post of height $5 \mathrm{m}$. A bullet of mass $0.01 \mathrm{kg}$, travelling with a velocity $V \mathrm{m} {\mathrm{s}}^{-1}$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of $20 \mathrm{m}$ and the bullet at a distance of $100$ $\mathrm{m}$ from the foot of the post. The initial velocity $V$ of the bullet is

Three blocks$A, B$ and $C$ are lying on a smooth horizontal surface, as shown in the figure. $A$ and $B$ have equal masses, $m$ and $C$ has mass $M$. Block $A$ is given an initial speed $v$ towards $B$ due to which it collides with $B$ perfectly inelastically. The combined mass collides with $C$, also perfectly inelastically. $\frac{5}{6}$$\mathrm{th}$ of the initial kinetic energy is lost in the whole process. What is value of $\frac{M}{m}$ ?

The position vector of the centre of mass $\overrightarrow{r} \mathrm{cm}$ of an asymmetric uniform bar of a negligible area of cross-section, as shown in the figure is:
 

The figure shows the position-time $(x-t)$ graph of one-dimensional motion of a body of mass $0.4 \mathrm{kg}$. The magnitude of each impulse is,