Impulse

A cannon of mass $M$ starts sliding freely down a smooth inclined plane at an angle $\alpha$ to the horizontal. After the cannon covered the distance $l$, a shot was fired, the shell leaving the cannon in the horizontal direction with a momentum $p$. As a consequence, the cannon stopped instantly. Assuming the change in mass of the canon to be negligible due to shot, determine the duration of the shot.

Two balls $A$ and $B$ of masses $1 \mathrm{kg}$ each are connected by an inextensible massless string. The system is resting on a smooth horizontal surface. An impulse of $10 \mathrm{N} \mathrm{s}$ is applied to the ball A at an angle $30°$ with the line joining two balls in horizontal direction as shown in the figure. Assuming that the string remains taut after impulse, if the magnitude of kinetic energy of ball $A$ is $\frac{175}{k}$. Find the value of  '$k$'.

A ball of $1 \mathrm{kg}$ drops vertically on the floor with a speed of $25 \mathrm{m}/\mathrm{s}$. It rebounds with a velocity of $10{ \mathrm{ms}}^{-1}$.

What impulse acts on the ball during contact?

A large force is acting on a body for a short time. The impulse imparted is equal to the change in _____.

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 large force is acting on a body for a short time. The impulse imparted is equal to the change in _____.

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

A cart is initially at rest and may roll freely. A $10 \mathrm{kg}$ package drops into a $25 \mathrm{kg}$ cart with a velocity of $3 \mathrm{m}/\mathrm{s}$. Determine  $\left(a\right)$ the final velocity of the cart, $\left(b\right)$ the impulse exerted by the cart on the package, $\left(c\right)$ the fraction of the initial energy lost in the impact.

A ball of mass $m$ strikes a rigid wall with speed $u$ at an angle of $30°$ with the normal and gets reflected with the same speed and at the same angle, as shown in the figure. If the ball is in contact with the wall for time $t$, then the force experienced by the wall is:

A block of the mass of $\mathrm{1\; kg}$ is moving on the $x$-axis. A force $F$ acting on the block is shown. The velocity of the block at time $t=2\mathrm{ }\mathrm{s}$ is $-3 \mathrm{m} {\mathrm{s}}^{-1}$. What is the speed of the block at time $t=4\mathrm{ }\mathrm{s}$?

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

A particle of mass $m$ is moving with a uniform velocity ${\nu }_1$ . It is given an impulse such that its velocity becomes ${\nu }_2$ . The impulse is equal to

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