Impulsive Forces in Collision

Q. A rigid ball of mass $m$ strikes a wall at ${60}^{\circ }$ and gets reflected without loss of speed as shown in figure. The value of impulse imparted by the wall on the ball will be:

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

Q.

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

1. $1.5mv$

2. $2mv$

3. zero

4. $1mv$

Q. The velocity $-$ time graph of a linear motion is shown in figure. The distance from the starting point after $8$ sec is

1. $16m$
2. $19m$
3. $8m$
4. $5m$

Q.

A pulse travelling on a string is represented by the function $y=\frac{a^3}{{(x-vt)}^2+a^2}$ where $a=5mm$ and $v=20cm{s}^{-1}$. Sketch the shape of the string at $t=0,1s$ and $2s$. Take $x=0$ in the middle of the string.

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

Q. A man generates a symmetrical pulse in a string by moving his hand up and down. At $t=0$, the point on his hand moves downward. The pulse travels with speed of $3\text{m/s}$ on the string & his hands passes 6 times in each second from the mean position. Then at what time the point on the string at a distance $3\text{m}$ from the hand will reach its upper extreme first time?

1. $\frac{13}{12}\text{sec}$
2. $1.25\text{sec}$
3. $1\text{sec}$
4. $1.4\text{sec}$

Q.

A shell is fired from cannon with a velocity 'V' at an angle $\theta$ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon. The speed of the other piece immediately after the explosion is

1. 

2. 

3. 

4. 

Q.

A ball is dropped from a height. It takes 0.200 s to cross the last 6.00 before hiting the ground, find the height from which it was dropped. Take $g=10m/s^2$

Q.

A bullet in motion hits and gets embedded in a solid, resting on a frictionless table. What is conserved

1. Momentum and K.E.

2. Momentum alone

3. K.E. alone

4. None of these

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.

During a heavy rain, hailstones of average size 1.0 cm in diameter fall with an average speed of 20 m/s.Suppose 2000 hailstones strike every square meter of a $10m\times 10m$ roof perpendicularly in one second and assume that the hailstones do not rebound.Calculate the average force exerted by the falling hailstones on the roof.Density of a hailstone is 900 $\frac{kg}{m^3}$.

Q. What is impulse and its applications?

Q. The acceleration-time graph of a particle moving in a straight line is as shown in the figure. The velocity of the particle at time $\text{t}=0$ is $2\text{m/s}$. The velocity after $2$ seconds will be

1. $2\text{m/s}$
2. $6\text{m/s}$
3. $4\text{m/s}$
4. $8\text{m/s}$

Q.

The average force necessary to stop a bullet of mass $20g$ moving with a speed of $250m/s$, as it penetrates into the wood for a distance of $12cm$ is

Q.

Two billiard balls each of mass 0.05 kg moving in opposite directions with speed $6m{s}^{-1}$ collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?

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.

What is impulse equal to?

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

Q. As shown in the figure, a body of mass $m$ moving vertically with a speed of $3\text{m/s}$ hits a smooth fixed inclined plane and rebounds with a velocity $v_f$ in horizontal direction. If angle of inclination is ${30}^{\circ }$, the velocity $v_f$ will be:

1. $3\text{m/s}$
2. $\frac{1}{\sqrt{3}}\text{m/s}$
3. this is not possible.
4. $\sqrt{3}\text{m/s}$

Q. A 0.5 kg block slides from the point A (see figure) on a horizontal track with an inital speed of 3 m/s towards a weightless horizontal spring of length 1 m and force constant 2 N/m. The part AB of the track is fictionless and the part BC has the coefficients of static and kinetic friction as 0.22 and 0.2 respectively. If the distances AB and BD are 2 m and 2.14 m respectively, then

1. frictional force on the block when it comes to rest is 0.2 N.
2. total distance travelled by the block is 4.24 m.
3. total compression of spring is 2 m.
4. frictional force of the block is 5.2 N.

Q.

The value of $g$ on the top of Mount Everest (height $8848m$) will be:

[Take radius of earth $6400000m$ and $g_{earth}=9.8m{s}^{-2}$]

1. $9.77m{s}^{-2}$

2. $6.77m{s}^{-2}$

3. $6.67m{s}^{-2}$

4. $5.77m{s}^{-2}$

Q.

The dot product of force and velocity is called:

1. work

2. power

3. energy

4. momentum

Q.

A uniform plate of mass M stays horizontally and symmetrically on two wheels rotating in opposite directions (figure 12-E16). The separation between the wheels is L. The friction coefficient between each wheel and the plate is $\mu .$ Find the time period of oscillation of the plate if it is slightly displaced along its length and released.

Q.

A body of mass 'm' collides against a wall with a velocity 'v' and retraces its path with the same speed. The change in momentum is (take initial direction of velocity as positive)

1. Zero

2. Mv

3. - 2 Mv

4. 2Mv

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 block of mass 2 kg is moving with a constant velocity on a rough horizontal surface as shown in the figure. The work done by the friction when the block moves by 5m are……
In the above question, the work done by the 10N applied force is…..

Q. A bullet moving with speed $100\text{m/s}$ strikes a block and get embedded into it. If mass of the block is nine times that of the bullet, find the impulse imparted by the bullet to the block (in $\text{Ns}$), given mass of the bullet is $m\text{kg}$.

1. $100\text{m}$
2. $90\text{m}$
3. $10\text{m}$
4. $110\text{m}$

Q. A body starts from rest from the origin with an acceleration of $3\frac{m}{s^2}$ along the $x$-axis and $4\frac{m}{s^2}$ along the $y$-axis. Its distance from the origin after 2$s$ will be

1. $15m$
2. $5m$
3. $10m$
4. $20m$

Q. A ball of mass $0.15\text{kg}$ hits the wall with its initial speed of $12{\text{ms}}^{-1}$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is $100\text{N}$, calculate the time duration of the contact of ball with the wall.

1. $0.036\text{s}$
2. $0.018\text{s}$
3. $0.072\text{s}$
4. $0.009\text{s}$