Bullets of mass $50 \, g$ are fired from a gun of mass $10 \, kg$ with a velocity of $300 \, m/s$. If $5$ bullets are fired per second,then what force must a person apply on the gun so that it does not recoil? $(N)$

$A$ metal block of $2 \,kg$ is at rest on a smooth plane. It is struck by a water jet releasing water at a rate of $1 \,kg \,s^{-1}$ with a speed of $5 \,ms^{-1}$. The acceleration of the block is: (in $\,ms^{-2}$)

$A$ Diwali cracker releases $25 \text{ g}$ of gas per second with a speed of $400 \text{ m/s}$ after an explosion. The force exerted by the gas on the cracker is:

$A$ rocket with a lift-off mass $2 \times 10^4\,kg$ is blasted upwards with an initial acceleration of $5\,m\,s^{-2}$. The initial thrust of the blast is (Take $g = 10\,m\,s^{-2}$).

An ice block is melting at a constant rate $\left| \frac{dm}{dt} \right| = \mu$. Its initial mass is $m_0$ and it is moving with velocity $v$ on a frictionless horizontal surface. The distance travelled by it until it melts completely is:

$A$ machine gun is mounted on a $2000 \,kg$ car on a horizontal frictionless surface. At some instant,the gun fires bullets of mass $10 \,g$ with a velocity of $500 \,m/s$ with respect to the car. The number of bullets fired per second is $10$. The average thrust on the system is ........ $N$.