Instantaneous Force and Impulse

Q. A thin uniform rod of mass $m$ and length $l$ is kept on a smooth horizontal surface such that it can move freely. At what distance $x$ from the centre of the rod should a particle of mass $m$ strike on the rod such that the point $P$ at a distance $\frac{l}{3}$ from the end of the rod is instantaneously at rest just after the elastic collision ?

1. $\frac{l}{2}$
2. $\frac{l}{3}$
3. $\frac{l}{6}$
4. $\frac{l}{4}$

Q. A hammer of weight $2\text{kg}$, moving with velocity $8\text{m/s}$, strikes against the head of a spike, and drives it into a block of wood. If hammer comes to rest in $0.02\text{sec}$, the impule associated with the spike will be:

1. $30\text{Ns}$
2. $-16\text{Ns}$
3. $-30\text{Ns}$
4. $16\text{Ns}$

Q. The figure shows the position-time (x-t) graph of one-dimensional motion of a particle of mass 0.4 kg. Find the magnitude of impulse imparted to the particle at $t=2\text{s}\text{and}4\text{s}$ respectively.

1. $0.2\text{Ns}$ and $0.4\text{Ns}$
2. $0.4\text{Ns}$ and $0.4\text{Ns}$
3. $0.8\text{Ns}$ and $0.4\text{Ns}$
4. $0.8\text{Ns}$ and $0.8\text{Ns}$

Q. A metal plate of mass $200gm$ is balanced in mid–air by throwing $40$ balls/sec, each of mass $2gm$, vertically upwards from below. The balls rebound with the same speed with which they strike the plate. Find the velocity with which the balls strike the plate. (Take $g=10m/s^2$)

1. $20m/s$
2. $12.5m/s$
3. $10m/s$
4. $5m/s$

Q. A hockey player applies an average force of $60\text{N}$ to $250\text{g}$ hockey puck for a time of $100\text{ms}$. The impulse experienced by the hockey puck is

1. $8\text{N-s}$
2. $6\text{N-s}$
3. $12\text{N-s}$
4. $10\text{N-s}$

Q. A metal plate of mass $200gm$ is balanced in mid–air by throwing $40$ balls/sec, each of mass $2gm$, vertically upwards from below. The balls rebound with the same speed with which they strike the plate. Find the velocity with which the balls strike the plate. (Take $g=10m/s^2$)

1. $20m/s$
2. $12.5m/s$
3. $10m/s$
4. $5m/s$

Q. A gun fires $10$ bullets/sec each of mass $10gm$, with a muzzle velocity of $50m/s$. Find the force required to hold the gun in position.

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

1. $24\text{N}$
2. $240\text{N}$
3. $300\text{N}$
4. $1200\text{N}$

Q. A ball moving with a momentum of $5\text{kg m/s}$ strikes against a wall at an angle of 45° and is reflected at the same angle. Calculate the change in momentum (in magnitude).

1. $7.07\text{kg m/s}$
2. $14.04\text{kg m/s}$
3. $3.53\text{kg m/s}$
4. $28.08\text{kg m/s}$

Q. A ball of mass $100\text{g}$ is projected with a velocity of $50\text{m/s}$ at ${37}^{\circ }$ from horizontal. Using the concept of impulse, find the magnitude of change in velocity of ball in $2\text{s}$ (Take g = 10 m/s${}^2$)

1. $70\text{m/s}$
2. $20\text{m/s}$
3. $30\text{m/s}$
4. $10\text{m/s}$

Q. A metal plate of mass $200\text{gm}$ is balanced in mid – air by throwing 40 balls /sec, each of mass $2\text{gm}$, vertically upwards from below. The balls rebound with the same speed with which they strike the plate. Find the velocity with which the balls strike the plate. (Take $g=9.8m/s^2$)

1. $20\text{m/s}$
2. $12.25\text{m/s}$
3. $10\text{m/s}$
4. $5\text{m/s}$

Q. A $10\text{g}$ bullet moving at $100\text{m/s}$ strikes a log. Assume that bullet undergoes uniform deacceleration and stops in $6.0\text{cm}$, find the magnitude of average force experienced by the log.

1. $600\text{N}$
2. $1233.33\text{N}$
3. $833.3\text{N}$
4. $1266.66\text{N}$

Q. A ball of mass $50\text{g}$ is dropped from a height of $20\text{m}$. A boy on the ground hits this ball vertically upward with a bat with an average force of $200\text{N}$ so that it attains a vertical height of $45\text{m}$. The time for which the ball remains in contact with this bat is
$[$Take $g=10{\text{m/s}}^2]$

1. $0.0325\text{s}$
2. $0.0025\text{s}$
3. $0.0125\text{s}$
4. $0.0225\text{s}$

Q.

In a cricket match, Sachin hit a 1 kg ball thrown at him at 126 km/hr exactly in the opposite direction with the exact same speed. Find the impulse that his bat imparted on the ball in the short duration for which they were in contact.

1. 35 N

2. 70 N

3. 35 Ns

4. 70 Ns

Q. An impulsive force $\left(F\right)$ acts on a body which changes with time $\left(t\right)$. The $F-t$ graph is shown below. The value of impulse in time $\pi \text{sec}$ will be:

1. $350\text{N-s}$
2. $200\text{N-s}$
3. $250\text{N-s}$
4. $300\text{N-s}$

Q. The displacement – time graph of a body of mass $2\text{kg}$ is shown. Find the impulse acting on the body in the time interval $t=2\text{sec}$ to $t=6\text{sec}$

1. $2\sqrt{3}kgm/s$
2. $(\sqrt{3}+1)kgm/s$
3. $(\sqrt{3}-1)kgm/s$
4. $2(\sqrt{3}-1)kgm/s$

Q. The figure shows the position-time (x-t) graph of one-dimensional motion of a particle of mass 0.4 kg. Find the magnitude of impulse imparted to the particle at $t=2\text{s}\text{and}4\text{s}$ respectively.

1. $0.2\text{Ns}$ and $0.4\text{Ns}$
2. $0.4\text{Ns}$ and $0.4\text{Ns}$
3. $0.8\text{Ns}$ and $0.4\text{Ns}$
4. $0.8\text{Ns}$ and $0.8\text{Ns}$

Q. A truck of mass $2000kg$ travelling at $4\text{m/s}$ comes to rest in $2\text{s}$ when it strikes a wall. Force exerted by the wall is

1. $2kN$
2. $1kN$
3. $4kN$
4. $8kN$

Q. A body is moving with velocity $30\text{m/s}$. A variable force $a\text{N}$ is applied at $t=0\text{s}$ on the body such that it increases it's velocity to $90\text{m/s}$ at $t=4\text{s}$ in same direction. The variation of force with time is shown in graph.

If mass of body is $10kg$, find the value of $a$ (shown in graph)

1. $150\text{N}$
2. $100\text{N}$
3. $50\text{N}$
4. $125\text{N}$

Q. A ball of mass $100\text{g}$ is projected with a velocity of $50\text{m/s}$ at ${37}^{\circ }$ from horizontal. Using the concept of impulse, find the magnitude of change in velocity of ball in $2\text{s}$ (Take g = 10 m/s${}^2$)

1. $70\text{m/s}$
2. $20\text{m/s}$
3. $30\text{m/s}$
4. $10\text{m/s}$

Q. A gun fires $10$ bullets/sec each of mass $10gm$, with a muzzle velocity of $50m/s$. Find the force required to hold the gun in position.

1. $5N$
2. $50N$
3. $500N$
4. $5000N$

Q. Find the velocity of the body of mass $2kg$ from the momentum-time graph at the end of $5$ seconds.

1. $10m/s$
2. $15m/s$
3. $20m/s$
4. $30m/s$

Q. A $10\text{g}$ bullet moving at $100\text{m/s}$ strikes a log. Assume that bullet undergoes uniform deacceleration and stops in $6.0\text{cm}$, find the magnitude of average force experienced by the log.

1. $600\text{N}$
2. $1233.33\text{N}$
3. $833.3\text{N}$
4. $1266.66\text{N}$

Q. In the figure given the position-time graph of a particle of mass $0.1\text{kg}$ is shown. The impulse at $t=2\text{s}$ is :

1. $0.2\text{kg-m/s}$
2. $-0.2\text{kg-m/s}$
3. $0.1\text{kg-m/s}$
4. $-0.4\text{kg-m/s}$

Q. A ball of mass $m=0.2\text{kg}$ is moving with velocity $v_i=60\text{m/s}$ and a force acts on the ball for a instant and changed its velocity to $v_f=90\text{m/s}$ in same direction. Find the impulse imparted to the ball.

1. 6 N-s
2. 3 N-s
3. 5 N-s
4. 4 N-s