A diwali rocket is ejecting $0.05\mathrm{kg}$ of gases per second at a velocity of $400 \mathrm{m} {\mathrm{s}}^{-1}$. The accelerating force on the rocket is

A ball weighing $10 \mathrm{g}$ hits a hard surface vertically with a speed of $5 \mathrm{m} {\mathrm{s}}^{-1}$ and rebounds with the same speed. the ball remains in contact with the surface for $0.01 \mathrm{s}$, then the average force exerted by the surface on the ball is :-

In the figure, the blocks $A, B$ and $C$ of mass $\mathrm{m}$ each have acceleration $a_1, a_2$ and $a_3$ respectively. $F_1$ and$F_2$ are external forces of magnitudes $2\mathrm{mg}$ and $\mathrm{mg}$ respectively :

A light string passes over a frictionless pulley. To one of its ends a mass of $6 \mathrm{kg}$ is attached and to its other end a mass of $10 \mathrm{kg}$ is attached. The tension in the string will be -

Calculate the acceleration of the mass $12 \mathrm{kg}$ shown in the set-up of fig, Also calculate the tension in the string connecting the $12 \mathrm{kg}$ mass. The string is weightless and inextensible, the pulleys are weightless and frictionless, angle of inclination is ${30}^{°}$.

Two masses of $4 \mathrm{kg}$ and $5 \mathrm{kg}$ are connected by a string passing through a frictionless pulley and are kept on a frictionless table as shown in the figure. The acceleration of $5 \mathrm{kg}$ mass is,