$A$ Diwali rocket is ejecting $0.05\, kg$ of gases per second at a velocity of $400\, m/s$. The accelerating force on the rocket is

$A$ rocket with an initial mass $m_0$ is going up with a constant acceleration $a$ by exhausting gases with a velocity $v$ relative to the rocket motion. The mass of the rocket at any instant of time $t$ is (assume that no other forces act on it).

$A$ heap of rope with mass density $\lambda$ (per unit length) lies on a table. You grab one end and pull horizontally with constant speed $v$,as shown in the figure. (Assume that the rope has no friction with itself in the heap.) The force that you must apply to maintain the constant speed $v$ is

$A$ flat plate moves normally with a speed $v_1$ towards a horizontal jet of water of uniform area of cross-section. The jet discharges water at the rate of volume $V$ per second at a speed of $v_2$. The density of water is $\rho$. Assume that water splashes along the surface of the plate at right angles to the original motion. The magnitude of the force acting on the plate due to the jet of water is

$A$ rocket is fired upward from the earth's surface such that it creates an acceleration of $20\, m/s^2$. If after $5\, s$ its engine is switched off,the maximum height of the rocket from the earth's surface would be......$m$

$A$ balloon and its content having mass $M$ is moving up with an acceleration $a$. The mass that must be released from the content so that the balloon starts moving up with an acceleration $3a$ will be: (Take $g$ as acceleration due to gravity)