$A$ $100 \, kg$ gun fires a ball of $1 \, kg$ horizontally from a cliff of height $500 \, m$. It falls on the ground at a distance of $400 \, m$ from the bottom of the cliff. Find the recoil velocity of the gun. (Acceleration due to gravity $g = 10 \, m/s^2$) (in $, m/s$)

$A$ particle of mass $m$ is acted upon by a force $F$ given by the empirical law $F = \frac{R}{t^2} v(t)$. If this law is to be tested experimentally by observing the motion starting from rest,the best way is to plot:

Match the items in Column-$I$ with those in Column-$II$.

Column-$I$	Column-$II$
$(1)$ Newton's third law of motion	$(a)$ $\vec{F}_{12} = -\vec{F}_{21}$
$(2)$ Law of conservation of momentum	$(b)$ $\Delta \vec{p} = 0$
	$(c)$ $\vec{F}_{12} = \vec{F}_{21}$

Can the work done by a frictional force be positive or negative?

$10,000$ small balls,each weighing $1 \, g$,strike $1 \, cm^2$ of area per second with a velocity of $100 \, m/s$ in a normal direction and rebound with the same velocity. The value of pressure on the surface will be:

$A$ solid ball is suspended from the ceiling of a motor car through a light string. $A$ transverse pulse travels at the speed $60 \text{ cm/s}$ on the string, when the car is at rest. When the car accelerates on a horizontal road, the speed of the pulse is $66 \text{ cm/s}$. The acceleration of the car is nearly $\left(g=10 \text{ m/s}^2\right)$ (in $\text{ m/s}^2$)