Impulsive Forces in Collision

Q. A system of two blocks $A$ and $B$ are connected by an inextensiible massless string as shown in figure. The pulley is massless and frictionless. Initially, the system is at rest. A bullet of mass $m$ moving with a velocity $u$ as shown in the figure hits block $B$ and gets embedded into it. Then find out the impulse imparted by tension force to the block of mass $3m$, immediately after the collision takes place.

1. $\frac{5}{4}mu$
2. $\frac{4}{5}mu$
3. $\frac{2}{5}mu$
4. $\frac{3}{5}mu$

Q. Velocity of a particle of mass $2\text{kg}$ changes from $\overrightarrow{v_1}=-2\hat{i}-2\hat{j}\text{m/s}$ to $\overrightarrow{v_2}=(\hat{i}-\hat{j})\text{m/s}$ after colliding with a plane surface. Then

1. The angle made by the plane surface with the positive $x-$axis is ${90}^{\circ }+{\tan }^{-1}\left(\frac{1}{3}\right)$
2. The angle made by the plane surface with the positive $x-$axis is ${\tan }^{-1}\left(\frac{1}{3}\right)$
3. The direction of change in momentum makes an angle ${\tan }^{-1}\left(\frac{1}{3}\right)$ with the positive $x-$ axis
4. The direction of change in momentum makes an angle ${90}^{\circ }+{\tan }^{-1}\left(\frac{1}{3}\right)$ with the plane surface.

Q. A particle of mass $2\text{kg}$ moving with a velocity of $3\text{m/s}$ is acted upon by a force which changes its direction of motion by an angle of ${90}^{\circ }$ without changing its speed. What is the magnitude of impulse experienced by the particle?

1. $6\text{N-s}$
2. $2\text{N-s}$
3. $3\sqrt{2}\text{N-s}$
4. $6\sqrt{2}\text{N-s}$

Q. A car of mass $1\times {10}^3\text{kg}$ travelling at a velocity $5\text{m/s}$ comes to rest in $2\text{sec}$, when it strikes a wall. What is the force exerted by the wall on car?

1. $2\times {10}^3\text{N}$
2. $2.5\times {10}^3\text{N}$
3. $5\times {10}^3\text{N}$
4. $4\times {10}^3\text{N}$

Q. Two balls of masses $2\text{kg}$ and $4\text{kg}$ after the collision are moving with speeds $4\text{m/s}$ and $2\text{m/s}$ as shown in figure. Find the impulse of reformation for the $4\text{kg}$ ball.

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

Q.

A lead ball strikes a wall and falls down but a tennis ball having the same mass and velocity striking the wall, bounces back. Check the correct statement.

1. The momentum of the lead ball is greater than that of the tennis ball

2. The lead ball suffers a greater change in momentum compared with the tennis ball

3. The tennis ball suffers a greater change in momentum as compared with the lead ball

4. Both suffer an equal change in momentum

Q. A block is moving under the influence of a constant force $F=3600\text{N}$. The force acts on the ball for the duration of $0.004\text{h}$. The average impulse imparted by the force is

1. $14400\text{N s}$
2. $51840\text{N s}$
3. $0.004\text{N s}$
4. $2844\text{N s}$

Q.

Two balls at same temperature collide. What is conserved?

1. Temperature

2. Velocity

3. Kinetic energy

4. Momentum

Q. A solid sphere is at rest on a horizontal surface. A horizontal impulse $J$ is applied at a height $h$ from the centre. The sphere starts rolling just after the application of impulse. The ratio $\frac{h}{R}$ will be

1. $\frac{2}{5}$
2. $\frac{1}{3}$
3. $\frac{3}{5}$
4. $\frac{5}{2}$

Q. A uniform rod of mass $M$ has an impulse applied at right angles to one end. If the other end begins to move with speed $V$, the magnitude of the impulse is

1. $2MV/3$
2. $MV$
3. $MV/2$
4. $2MV$

Q.

A block of mass 'm' and a pan of equal mass are connected by a string going over a smooth light pulley as shown in figure. Initially the system is at rest when a particle of mass m falls on the pan and sticks to it. If the particle strikes the pan with a speed 'v' find the speed with which the system moves just after the collision.

1. $\frac{v}{2}$

2. $\frac{v}{3}$

3. $\frac{v}{6}$

4. $2\frac{v}{3}$

Q. A force-time graph for a body (starting from rest) moving along a straight line in $1\text{D}$ is shown in figure. The linear momentum gained by body during time interval $0\text{s}$ to $6\text{s}$ is

1. $2\text{N.s}$
2. $4\text{N.s}$
3. $6\text{N.s}$
4. Zero

Q.

A ball of mass 0.4 kg moving with uniform speed of $2m{s}^{-1}$ strikes normally a wall and rebounds. Assuming the collision to be elastic and the time of contact of the ball with the wall as 0.4s, find the force exerted on the ball

1. 1 N

2. 2 N

3. 3 N

4. 4 N

Q. A system of two blocks $A$ and $B$ are connected by an inextensiible massless string as shown in figure. The pulley is massless and frictionless. Initially, the system is at rest. A bullet of mass $m$ moving with a velocity $u$ as shown in the figure hits block $B$ and gets embedded into it. Then find out the impulse imparted by tension force to the block of mass $3m$, immediately after the collision takes place.

1. $\frac{5}{4}mu$
2. $\frac{4}{5}mu$
3. $\frac{2}{5}mu$
4. $\frac{3}{5}mu$

Q. A bowler bowled a ball of mass $0.2\text{kg}$ at a speed of $162\text{km/h}$. The batsman played a defensive shot and the ball came to rest after striking the bat. If the contact between the ball and the bat is for $0.015\text{s}$, find the magnitude of the impulsive force applied by the bat on the ball.

1. $3000\text{N}$
2. $4500\text{N}$
3. $1500\text{N}$
4. $6000\text{N}$

Q. Two balls of masses $2\text{kg}$ and $4\text{kg}$ are moved towards each other with velocities $4\text{m/s}$ and $2\text{m/s}$ respectively on a frictionless surface. Find the impulse of maximum deformation for the ball of $4\text{kg}$ mass.

1. $\frac{8}{3}\text{N-s}$
2. $\frac{4}{3}\text{N-s}$
3. $\frac{2}{3}\text{N-s}$
4. $8\text{N-s}$

Q. A particle of mass $5\text{kg}$ is initially at rest. A force starts acting on it along a fixed direction. The magnitude of the force changes with time as shown in the figure. Find the velocity of the particle at the end of $20\text{s}$.

1. $10\text{m/s}$
2. $50\text{m/s}$
3. $100\text{m/s}$
4. $20\text{m/s}$

Q. A ball of mass $m$ is initially at rest. A variable force starts acting on it in a fixed direction, whose magnitude changes with time. The force - time graph is shown in the figure.


Find the speed of the ball at the end of time $t=T$ seconds.

1. $\frac{3}{5}v\text{m/s}$
2. $\frac{3}{4}v\text{m/s}$
3. $\frac{4}{3}v\text{m/s}$
4. $\frac{2}{3}v\text{m/s}$

Q. A ball of mass $2\text{kg}$ is dropped from a height of $20\text{m}$. After striking the ground, the ball bounces back with half of its striking speed. Find the impulse imparted by the normal reaction from the ground. Take $g=10{\text{m/s}}^2$.

1. $40\text{N-s}$
2. $80\text{N-s}$
3. $0\text{N-s}$
4. $60\text{N-s}$

Q. A particle of mass $5\text{kg}$ is initially at rest. A force starts acting on it along a fixed direction. The magnitude of the force changes with time as shown in the figure. Find the velocity of the particle at the end of $20\text{s}$.

1. $10\text{m/s}$
2. $50\text{m/s}$
3. $100\text{m/s}$
4. $20\text{m/s}$

Q. Two identical blocks $A$ and $B$, connected through a massless string are placed on a frictionless horizontal surface. A bullet having mass $2$ times that of a single block, moving with velocity $u$ strikes block $B$ from behind as shown in the figure. If the bullet comes to rest after striking the block, find the impulse on block $A$ due to tension in the string.

1. $\frac{mu}{2}$
2. $\frac{mu}{4}$
3. $mu$
4. $2mu$

Q. A hockey player receives a corner shot at a speed of $15\text{m/s}$ at angle ${30}^{\circ }$ with y - axis and then shoots the ball along x - axis with the speed $30\text{m/s}$. If the mass of the ball is $150\text{grams}$ and it remains in contact with the hockey stick for $0.01\text{s}$, the force exerted on the ball along x - axis is

1. $281\text{N}$
2. $187.5\text{N}$
3. $562.5\text{N}$
4. $375\text{N}$

Q. A ball of mass $1\text{kg}$ is attached to an inextensible string. The ball is released from the position shown in figure. Find the magnitude of impulse imparted by the string to the ball immediately after the string becomes taut. Take $g=10{\text{m/s}}^2$.

1. $4\sqrt{40}\text{N-s}$
2. $4\sqrt{10}\text{N-s}$
3. $4\sqrt{20}\text{N-s}$
4. $4\sqrt{5}\text{N-s}$

Q. A cubical block is moving on a horizontal smooth plane. It hits a ridge at point $\text{O}$. The angular speed of the block after it hits $\text{O}$ is

1. $10\text{rad/s}$
2. $18\text{rad/s}$
3. $12\text{rad/s}$
4. $15\text{rad/s}$

Q. A time varying force is represented as $F=2t\text{N}$. Find out the impulse imparted by this force during the first second.

1. $\frac{1}{2}\text{N.s}$
2. $1\text{N.s}$
3. $2\text{N.s}$
4. $4\text{N.s}$

Q. A ball of mass $2\text{kg}$ is dropped from a height of $20\text{m}$. After striking the ground, the ball bounces back with half of its striking speed. Find the impulse imparted by the normal reaction from the ground. Take $g=10{\text{m/s}}^2$.

1. $40\text{N-s}$
2. $80\text{N-s}$
3. $0\text{N-s}$
4. $60\text{N-s}$

Q. Two blocks of masses $m_1$ and $m_2$ are connected by a light inextensible string which passes over a fixed pulley. Initially, mass $m_1$ moves with a velocity $v_0$ when the string is not taut. Neglect friction at all contact surfaces. Find the velocity of the blocks just after the string is taut, if $m_1=2\text{kg},m_2=3\text{kg}$ and $v_0=5\text{m/s}$

1. $2\text{m/s}$
2. $3\text{m/s}$
3. $5\text{m/s}$
4. $0\text{m/s}$

Q. A child pushes a $2.2\text{kg}$ swing that is initially at rest. The net force on the swing over time is shown below.


What is the swing's speed at $t=40\text{ms}$? Round off the answer to two decimal places.

1. $0.36\text{m/s}$
2. $0.48\text{m/s}$
3. $0.15\text{m/s}$
4. $0.26\text{m/s}$

Q. Two balls of masses $2\text{kg}$ and $4\text{kg}$ are moved towards each other with velocities $4\text{m/s}$ and $2\text{m/s}$ respectively on a frictionless surface. Find the impulse of maximum deformation for the ball of $4\text{kg}$ mass.

1. $\frac{8}{3}\text{N-s}$
2. $\frac{4}{3}\text{N-s}$
3. $\frac{2}{3}\text{N-s}$
4. $8\text{N-s}$

Q. Two point masses connected by a light inextensible string are lying on a frictionless surface as shown in figure. An impulse of magnitude $10\text{kg m/s}$ is given to the $5\text{kg}$ block. Then:

1. Velocity of $10\text{kg}$ mass immediately after impulse is given is $\frac{1}{3}\text{m/s}$.
2. Velocity of $10\text{kg}$ mass immediately after impulse is given is $2\text{m/s}$.
3. Velocity of $5\text{kg}$ mass immediately after impulse is given is $\sqrt{\frac{28}{9}}\text{m/s}$.
4. Velocity of $5\text{kg}$ mass immediately after impulse is given is $\frac{\sqrt{28}}{9}\text{m/s}$.