A bomb of mass $3 m$ is kept inside a closed box of mass $3 m$ and length $4 L$ at its centre. It explodes in two parts of mass $\mathrm{m}$ and $2 m.$ The two parts move in opposite directions and stick to the opposite sides of the walls of box. The box is kept on a smooth horizontal surface. What is the distance moved by the box during this time interval? 

For the system shown in the figure, a small block of mass $\mathrm{m}$ and smooth irregular shaped block of mass $\mathrm{M},$ both free to move are placed on a smooth horizontal plane. The minimum velocity $\mathrm{v}$ imparted to block so that it will overcome the highest point of $\mathrm{M}$ is 

Two objects that are moving along an $x y$ -plane on a frictionless floor collide. Assume that they form a closed. isolated system. The following table gives some of the momentum components (in kilogram meters per second) before and after the collision. What are the missing values $\left(a, b\right)?$

Figure shows a hollow cube of side ' $\mathrm{a}$ ' and volume ' $\mathrm{V}.$ There is a small chamber of volume $\mathrm{V}/4$ in the cube as shown. The chamber is completely filled by $\mathrm{m} \mathrm{kg}$ of water. Water leaks through a hole $\mathrm{H}$ and spreads in the whole cube. Then the work done by gravity in this process assuming that the complete water finally lies at the bottom of the cube is

A block 'A' of mass $\mathrm{m},$ hits horizontally the rear side of a spring (ideal) attached to a block $B$ of mass $m_2$ resting on a smooth horizontal surface. After hitting, ' $A$ ' gets attached to the spring.

Some statements are given at any moment of time:
i. If velocity of $A$ is greater than $B,$ then kinetic energy of the system will be decreasing.
ii. If velocity of $A$ is greater than $B,$ then kinetic energy of the system will be increasing.
¡ii. If velocity of $A$ is greater than $B,$ then momentum of the system will be decreasing. iv. If velocity of $A$ is greater than $B,$ then momentum of the system will be increasing.
Now select correct alternative:

Two blocks of masses $\mathrm{m}$ and $4 \mathrm{m}$ lie on a smooth horizontal surface connected with a spring in its natural length. Mass $\mathrm{m}$ is given velocity $v_0$ through an impulse as shown in figure. Which of the following is not true about subsequent motion?

Two identical blocks, having mass $\mathrm{M}$ each, are conjugated and placed on a smooth floor as shown in figure. A small block of mass $\mathrm{m}$ is released from position as shown. Velocity of block $\mathrm{B}$ is maximum