Two blocks of masses $m_1$ and $m_2$ are connected by a spring of spring constant $k$,initially at their natural length as shown. $A$ sharp impulse is given to mass $m_2$ so that it acquires a velocity $v_0$ towards the right. If the system is kept on a smooth floor,find the maximum elongation that the spring will suffer.

Assertion $(A)$: In an elastic collision of two billiard balls,the total kinetic energy $(KE)$ is conserved during the short time of collision of the balls (i.e.,when they are in contact).
Reason $(R)$: Energy spent against friction does not follow the law of conservation of energy.

Equal force $F (> mg)$ is applied to the string in all the $3$ cases. Starting from rest,the point of application of force moves a distance of $2 \ m$ down in all cases. In which case does the block have maximum kinetic energy?

$A$ truck of mass $M$ and a car of mass $\frac{M}{10}$ moving with the same momentum are brought to a halt by the application of the same braking force. The ratio of the distances travelled by the truck and the car before they come to a stop is

$A$ block of mass $5 \ kg$ is lifted to a height of $5 \ m$ by a force of $60 \ N$. Find:
$(1)$ Work done by the force.
$(2)$ Potential energy of the block at $5 \ m$.
$(3)$ Kinetic energy of the block at $5 \ m$.
$(4)$ Velocity of the block at $5 \ m$. (Take $g = 9.8 \ m/s^2$)

Two balls,having linear momenta $\vec{p}_1 = p \hat{i}$ and $\vec{p}_2 = -p \hat{i}$,undergo a collision in free space. There is no external force acting on the balls. Let $\vec{p}_1^{\prime}$ and $\vec{p}_2^{\prime}$ be their final momenta. Which of the following option$(s)$ is (are) $NOT ALLOWED$ for any non-zero value of $p, a_1, a_2, b_1, b_2, c_1$ and $c_2$?
$(A)$ $\vec{p}_1^{\prime} = a_1 \hat{i} + b_1 \hat{j} + c_1 \hat{k}$,$\vec{p}_2^{\prime} = a_2 \hat{i} + b_2 \hat{j}$
$(B)$ $\vec{p}_1^{\prime} = c_1 \hat{k}$,$\vec{p}_2^{\prime} = c_2 \hat{k}$
$(C)$ $\vec{p}_1^{\prime} = a_1 \hat{i} + b_1 \hat{j} + c_1 \hat{k}$,$\vec{p}_2^{\prime} = a_2 \hat{i} + b_2 \hat{j} - c_1 \hat{k}$
$(D)$ $\vec{p}_1^{\prime} = a_1 \hat{i} + b_1 \hat{j}$,$\vec{p}_2^{\prime} = a_2 \hat{i} + b_1 \hat{j}$