$A$ balloon of total mass $M$ and a fixed size starts coming down with an acceleration $f$ $(f < g)$. The fraction of the total mass of the balloon which must be dropped from it so that it starts going up with an acceleration of $f$ (assuming negligible air resistance) is

$A$ box '$A$' is lying on the horizontal floor of the compartment of a train running along horizontal rails from left to right. At time '$t$',it decelerates. Then the reaction $R$ by the floor on the box is given best by

$A$ body of mass $3 \, kg$ hits a wall at an angle of $60^\circ$ with the wall and returns at the same angle. The speed of the body is $10 \, m/s$ and the impact time is $0.2 \, s$. Calculate the force exerted on the wall.

$A$ spring-block system is placed on a rough horizontal floor. The block is pulled towards the right to give the spring some elongation and then released.

$A$ bullet of mass $20 \, g$ travelling horizontally with a speed of $500 \, m/s$ passes through a wooden block of mass $10.0 \, kg$ initially at rest on a surface. The bullet emerges with a speed of $100 \, m/s$ and the block slides $20 \, cm$ on the surface before coming to rest. Find the coefficient of friction between the block and the surface. $(g = 10 \, m/s^2)$

$A$ body of mass $2 \ kg$ is initially at rest. It moves on a table under the influence of a horizontal force of $7 \ N$. If the coefficient of kinetic friction is $0.1$,then the work done by the applied force and the work done by the frictional force in $10 \ s$ are respectively: