The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium,the angle $\theta$ should be ........ $^o$.

$A$ 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.

$A$ 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

$A$ 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:

The mass of a hydrogen molecule is $3.32 \times 10^{-27} \ kg$. If $10^{23}$ hydrogen molecules strike,per second,a fixed wall of area $2 \ cm^2$ at an angle of $45^\circ$ to the normal,and rebound elastically with a speed of $10^3 \ m/s$,then the pressure on the wall is nearly:

What is the acceleration of the block and trolley system shown in the figure,if the coefficient of kinetic friction between the trolley and the surface is $0.04$? What is the tension in the string? (Take $g = 10\; m s^{-2}$). Neglect the mass of the string.