Two unequal masses $A$ and $B$ moving along a straight line are brought to rest by equal retarding forces. If $A$ takes double the time taken by $B$ to come to rest and $A$ travels $\frac{2}{3}$ of the distance covered by $B$ before coming to rest,then the ratio of masses of $A$ and $B$ is . . . . . . .

$A$ mass of $1 \text{ kg}$ is kept on an inclined plane with $30^\circ$ inclination with respect to the horizontal plane and it is at rest initially. Then,the whole assembly is moved up with a constant velocity of $4 \text{ m/s}$. The work done by the frictional force in time $2 \text{ s}$ is . . . . . . $\text{J}$. (Take $g = 10 \text{ m/s}^2$)

$A$ $100 \ kg$ 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. The recoil velocity of the gun is (Acceleration due to gravity $= 10 \ ms^{-2}$). (in $ms^{-1}$)

$A$ $10 \,g$ bullet moving at $200 \,m/s$ stops after penetrating $5 \,cm$ of a wooden plank. The average force exerted on the bullet will be .......... $N$.

$A$ car of mass $1250 \ kg$ is moving with a velocity of $30 \ m/s$. $A$ resistive force of $750 \ N$ acts on it. If the engine produces a power of $30 \ kW$,what is the acceleration of the car in $m/s^2$?

In the arrangement shown in the figure,if the blocks of masses $m$ and $2m$ are released from rest,find the tension in the string. (Given: $\mu_1 = 2/3$ for mass $m$,$\mu_2 = 1/3$ for mass $2m$,the string is massless and inextensible,and the pulley is frictionless.)