$A$ small disc of mass $m$ slides down with initial velocity zero from the top $(A)$ of a smooth hill of height $H$ having a horizontal portion $(BC)$ as shown in the figure. If the height of the horizontal portion of the hill is $h$,then the maximum horizontal distance covered by the disc from the point $D$ is

$A$ ball moving with speed $v$ hits another identical ball at rest. The two balls stick together after the collision. If the specific heat of the material of the balls is $S$,the temperature rise resulting from the collision is

$A$ body of mass $4 \,kg$ is moving with momentum of $8 \,kg \,m/s$. $A$ force of $0.2 \,N$ acts on it in the direction of motion of the body for $10 \,s$. The increase in kinetic energy in joules is

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.

$A$ ball is projected vertically upwards. Air resistance and variation in $g$ may be neglected. The ball rises to its maximum height $H$ in a time $T$,the height being $h$ after a time $t$.
[$1$] The graph of kinetic energy $E_k$ of the ball against height $h$ is shown in figure $1$.
[$2$] The graph of height $h$ against time $t$ is shown in figure $2$.
[$3$] The graph of gravitational potential energy $E_g$ of the ball against height $h$ is shown in figure $3$.
Which of the following shows the correct answers?

$A$ child swings on a swing such that the minimum and maximum heights from the ground are $0.75 \ m$ and $2 \ m$ respectively. The maximum velocity of the swing is ...... $ms^{-1}$.