Newton's Laws of Motion

A particle moves so that its acceleration is always twice its velocity. If its initial velocity is $0.1 \mathrm{m} {\mathrm{s}}^{-1}$, its velocity after it has gone $0.1 \mathrm{m}$ is

A body of mass $1 \mathrm{kg}$ moving with a uniform velocity of $1 \mathrm{m} {\mathrm{s}}^{-1}$. If the value of $g$ is $5 \mathrm{m} {\mathrm{s}}^{-2}$, then the force acting on the frictionless horizontal surface on which the body is moving is

A particle of mass $10 \mathrm{kg}$ is moving in a straight line. If its displacement, $x$ with time $t$ is given by $x=\left(t^3-2t-10\right) \mathrm{m}$ then the force acting on it at the end of $4 \mathrm{seconds}$ is

A body of mass $m=3.513 \mathrm{kg}$ is moving along the $x$-axis with a speed of $5.00 \mathrm{m} {\mathrm{s}}^{-1}$. The magnitude of its momentum is recorded as

A ball mass $m$ falls vertically to the ground from a height $h_1$ and rebounds to a height $h_2$. The change in momentum of the ball of striking the ground is

The linear momentum $P$ of a body moving in one dimension varies with time according to the equation $P=a+b{t}^2$ where $a$ and $b$ are positive constants. The net force acting on the body is

A force of $10 \mathrm{N}$ acts on a body of mass $20 \mathrm{kg}$ for $10$ seconds. Change in its momentum is

A particle of mass $m$ is moving with velocity $v_1$, it is given an impulse such that the velocity becomes $v_2$. Then magnitude of impulse is equal to

A machine gun has a mass $5 \mathrm{kg}$. It fires $50 \mathrm{gram}$ bullets at the rate of $30$ bullets per minute at a speed of $400 \mathrm{m} {\mathrm{s}}^{-1}$. What force is required to keep the gun in position?

A machine gun fires a bullet of mass $40 \mathrm{g}$ with a velocity $1200 \mathrm{m} {\mathrm{s}}^{-1}$. The man holding it can exert a maximum force of $144 \mathrm{N}$ on the gun. How many bullets can be fired per second?

A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $g/8$, then the ratio of the masses is

Speeds of two identical cars are $u$ and $4u$ at a specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is

If a body looses half of its velocity on penetrating $3 \mathrm{cm}$ in a wooden block, then how much will it penetrate more before coming to rest?

The mass of a body measured by a physical balance in a lift at rest is found to be $m$. If the lift is going up with an acceleration $a$, its mass will be measured as

A gun of mass $10 \mathrm{kg}$ fires $4$ bullets per second. The mass of each bullet is $20 \mathrm{g}$ and the velocity of the bullet when it leaves the gun is $300 \mathrm{m} {\mathrm{s}}^{-1}$. The force required to hold the gun while firing is

A player caught a cricket ball of mass $150 \mathrm{gm}$ moving at the rate of $20 \mathrm{m} {\sec }^{-1}$. If the catching process be completed in $0.1 \sec$, then the force exerted by the ball on the hands of player is

A bullet is fired from a gun. The force on the bullet is given by, $F=600-2\times {10}^{5}t$, where, $F$ is in newton and $t$ in second. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet?

A body of mass $M$ hits normally a rigid wall with velocity $V$ and bounces back with the same velocity. The impulse experienced by the body is

If $n$ bullets, each of mass $m$ are fired with a velocity $v$ per second from a machine gun, the force required to hold the gun in position is

A hammer weighing $3 \mathrm{kg}$ strikes the head of a nail with a speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$ drives it by $1 \mathrm{cm}$ into the wall. The impulse imparted to the wall is