Impulse

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

Two billiard ball each of mass $m \mathrm{kg}$ moving in opposite directions with speed $5 \mathrm{m} {\mathrm{s}}^{-1}$ collide and rebounds with the same speed. The magnitude of impulse imparted to each ball due to other is

Figure shows the position–time $(x-t)$ graph of one dimensional motion of a body of mass $500 \mathrm{g}$. What is the time interval between two consecutive impulses received by the body?

A batsman hits back a ball of mass $0.15 \mathrm{kg}$ straight in the direction of the bowler without changing its initial speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$. If the ball moves in same straight line, then the impulse imparted by it (in $\mathrm{N} \mathrm{s}$) is,

A rigid ball of mass $m$ elastically colides a rigid wall at ${60}^{\mathrm{o}}$ and gets reflected as shown in the figure. Find the impulse imparted by the wall on the ball.

The figure shows the position-time $(x-t)$ graph of one-dimensional motion of a body of mass $500\mathrm{ }\mathrm{g}.\mathrm{ }$The interval between two consecutive impulses received by the body would be

${10}^{22}$ gas molecules each of mass ${10}^{-26} \mathrm{kg}$ collide with a surface (perpendicular to it) elastically per second over an area $1 {\mathrm{m}}^2$ with a speed ${10}^4 \mathrm{m} {\mathrm{s}}^{-1},$ the pressure exerted by the gas molecules will be of the order of

At time $\mathrm{t}$ sec, a particle of mass $3 \mathrm{kg}$ has position vector $\overrightarrow{\mathrm{r}}=\left(3\mathrm{t}\hat{\mathrm{i}}-4\cos \mathrm{t}\hat{\mathrm{j}}\right)\mathrm{ }\mathrm{m}$. The impulse of the force during the time interval $0\le \mathrm{t}\le \frac{\mathrm{\pi }}{2}$ is

The magnitude of force acting on a body varies with time as shown in the figure. The magnitude of total impulse of the force on the body from $t=\; 0$ to $t=16 \mathrm{\mu s}$ is-

A solid ball of radius $0.2$$\mathrm{m}$ and mass $1$ $\mathrm{kg}$ lying at rest on a smooth horizontal surface is given an instantaneous impulse of $50$ $\mathrm{N} \mathrm{s}$ at point $\mathrm{P}$ as shown. The number of rotations made by the ball about its diameter before hitting the ground is

A particle of mass $m$ is moving in a straight line with momentum $p.$ Starting at time $t=0,$ a force $F=kt$ acts in the same direction on the moving particle during time interval $T$ so that its momentum changes from $p$ to $3p.$ Here $k$ is a constant. The value of $T$ is:

The one which does not represent a force in any context is

A ball of mass m hits a rough floor with a velocity $v$ as shown. The coefficient of friction is $\mu$ between the ball and the floor. Answer the questions that follow:

Find out the final velocity of the ball just after the collision. (perfectly inelastic collision)

A ball of mass m hits a rough floor with a velocity $v$ as shown. The coefficient of friction is $\mu$ between the ball and the floor. Answer the questions that follow:



Find out the impulse of the normal on the ball during the collision (for a perfectly inelastic collision)

A ball of mass m hits a rough floor with a velocity $v$ as shown. The coefficient of friction is $\mu$ between the ball and the floor. Answer the questions that follow:

If the collision is perfectly inelastic, the angle made by the velocity of the ball with the horizontal after the collision is

A body of mass 10 kg is acted upon by a given equation $F=\left(3t^2-30\right)$ Newton. The initial velocity of the body is 10 m/s. The velocity of the body after 5 sec is

The direction of impulse is

At time t second, a particle of mass 3 kg has position vector $\overrightarrow{r}$ metre where $\overrightarrow{r}=\mathrm{(3}\mathrm{t)} \widehat{i}-\mathrm{(4 }\mathrm{cos }\mathrm{t)}\widehat{j}$ . The impulse of the force during the time interval $0\le t\le \frac{\pi }{2}$is

A body of mass 5 kg is acted on by a net force F which varies with time t as shown in graph, then the net momentum in SI units gained by the body at the end of 10 seconds is

A body of $2 \mathrm{kg}$ has an initial speed $5\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ . A force acts on it for $4 \mathrm{seconds}$ in the direction of motion. The force-time graph is shown in figure. The final speed of the body after $4 \mathrm{s}$ is