Tag: work, energy and power

Questions Related to work, energy and power

Two equal masses ${m} _{1}$ and ${m} _{2}$ moving along the same straight line with velocities $+3  {m}/{s}$ and $-5  {m}/{s}$ respectively collide elastically. Their velocities after the collision will be respectively :

force exerted by collision collisions work, energy and power mechanics physics

  1. $+4 {m}/{s}$ for both

  2. $-3 {m}/{s}$ and $+5 {m}/{s}$

  3. $-4 {m}/{s}$ and $+4 {m}/{s}$

  4. $-5 {m}/{s}$ and $+3 {m}/{s}$

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Correct Option: D
Explanation:

As ${m} _{1} = {m} _{2}$, therefore after elastic collision velocities of masses gets interchanged.

A machine gun of mass 5 kg fires 30 bullets, each of mass 50 g, per minute at a speed of $400\,m\,{s^{ - 1}}$. What force must be exerted to keep the machine gun in position?

force exerted by collision collisions work, energy and power mechanics physics

  1. $30N$

  2. $10N$

  3. $27N$

  4. $33N$

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Correct Option: B
Explanation:

Mass of the gun $=5kg$

Mass of bullets $=50g$
speed at which the bullet is fired$=400m/s$
Therefore$,$ force required to keep the machine gun in position $=\frac{{ch\arg e\,in\,momentum\,of\,bullets}}{{time\,taken}}$
$=\frac{{\left( {50 \times {{10}^{ - 3}} \times 30} \right) \times 400}}{{60}} = 10\,N$
Hence,
option $(B)$ is correct answer.

Two particles of mass $M _{A} $ and $M _{B} $ and there velocities are $V _{A} $ and $V _{B} $ respectively collides. After collision they inter changes their velocities then ratio of  $\dfrac{M _{A}}{M _{B}}$ is:

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. (a) $\dfrac{V _{A}}{V _{B}}$

  2. (b) $\dfrac{V _{B}}{V _{A}}$

  3. (c) $\dfrac{V _{A}+V _{B}}{V _{B}-V _{A}}$

  4. (d) 1

Show answer
Correct Option: A
Explanation:
The correct option is B.

Given


Two particles having mass $M _a \& M _b$ and the velocities are $V _a\$V_b$

so when the collides then they interchange their velocities.

Thus the ratio of their velocities after collission is :

$\dfrac{V_a}{V_b}$

A plastic ball falls from a height of $4.9$ metre and rebounds several times from the floor. What is the coefficient of restitution during the impact with the floor if $1.3$ seconds pass from the first impact to the second one?

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. $0.9$

  2. $0.1$

  3. $0.7$

  4. $0.8$

Show answer
Correct Option: B
Explanation:
As, $ t = \sqrt{\dfrac{2h}{g}} $
Velocity of ball just before collision $ = v = \sqrt{2gh} $
After first collision,
Velocity $ = v _{1} = ev = e\sqrt{2gh} $
So, $ t _{1} = \dfrac{v _{1}}{g} = e \sqrt{\dfrac{2h}{g}} $
So, time for second collision will be 
$ T = t+2t _{1} $
$ = (1+2e)\sqrt{\dfrac{2h}{g}} $
Putting, $ T = 1.3\,sec.,h = 4.9\,m $
$ 1.3 = (1+2e)\sqrt{\dfrac{2\times 4.9}{9.8}} $
$ 1.3 = 1+2e $
$ 0.3 = 2e $
$ \boxed{e = 0.1} $ 

As shown in figure a particle is released from highest point of curved smooth path. Find the distance of point of strike from $A$.

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. $10\ m$

  2. $5\ m$

  3. $20\ m$

  4. $none\ of\ these$

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Correct Option: C

A body 'x' with a momentum 'p' collides with with another identical stationary body 'y' dimensionally. During the collision 'y' gives an impulse 'J' to the body 'x'. Then the coefficient of restitution is 

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. $\dfrac p{p-2J}$

  2. $\dfrac p{p-J}$

  3. $\dfrac p{p+2J}$

  4. $\dfrac p{p+J}$

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Correct Option: A

A uniform rod AB of length $L$ and mass $M$ is lying on a smooth table. A small particle of mass $m$ strike the rod with a velocity $v _0$ at point C a distance x from the centre O. The particle comes to rest after collision. The value of $x$, so that point A of the rod remains stationary just after the collision,  is:

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. $L/3$

  2. $L/6$

  3. $L/4$

  4. $L/12$

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Correct Option: B

a body of mass m falls from height h on ground. If e be the coefficient of restitution of collision betwwen the body and ground then the distance travelled by body before it comes to rest is

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. $h\left{ {\dfrac{{1\, + {e^2}}}{{1 - {e^2}}}} \right}$

  2. $h\left{ {\dfrac{{1\, - {e^2}}}{{1 + {e^2}}}} \right}$

  3. ${\dfrac{{2eh}}{{1 + {e^2}}}}$

  4. ${\dfrac{{2eh}}{{1 - {e^2}}}}$

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Correct Option: C

A solid spherical ball of radius R collides with a rough horizontal surface as shown in figure. At the time of collision its velocity is $v _{0}$ at an angle $\theta$ to the horizontal and angular velocity $\omega _{0}$ as shown. After collision, angular velocity of ball may

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. decrease

  2. increase

  3. remains constant

  4. none of these

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Correct Option: A

A particle of mass $M$ is moving in a horizontal circle of radius $R$ with uniform speed $v$. When it moves from one point to a diametrically opposite point, its:

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. momentum does not change

  2. momentum changes by $2Mv$

  3. $KE$ changes by $Mv^{2}$

  4. none of the above

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Correct Option: B