Tag: collision of two rigid bodies

Questions Related to collision of two rigid bodies

A uniform rod AB of mass $3m$ and length $2l$ is lying at rest on a smooth horizontal table with a smooth vertical axis through the end $A$ . A particle of mass $2m$ moves with speed $2u$ across the table and strikes the rod at its mid point $C$. If the impact is perfectly elastic , then find the speed of the particle after impact if it strikes the rod normally 

physics momentum collision of two rigid bodies energy and collisions understanding collisions

  1. $\dfrac{7u}{3}$

  2. $\dfrac{2u}{3}$

  3. $\dfrac{u}{3}$

  4. $\dfrac{4u}{3}$

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Correct Option: C

A body falls from height 20 m.If coefficient of restitution 1/2. The time interval between starting point and second bounce is $\left( {g = 10\;m{s^{ - 2}}} \right)$

physics momentum collision of two rigid bodies energy and collisions understanding collisions

  1. 1 s

  2. 2 s

  3. 3 s

  4. 4 s

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Correct Option: C

A disc of mass $100g$ and radius $10cm$ has a projection on its circumference. The mass of projection is negligible. A $20g$ bit of putty moving tangential to the disc with a velocity of $5m{s}^{-1}$ strikes the projection and sticks to it. The angular velocity of disc is

physics momentum collision of two rigid bodies energy and collisions understanding collisions

  1. $14.29rad{s}^{-1}$

  2. $17.3rad{s}^{-1}$

  3. $12.4rad{s}^{-1}$

  4. $9.82rad{s}^{-1}$

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Correct Option: A

Two spheres $A$ and $B$ of masses $m _1$ and $m _2$ respectively collide. $A$ is at rest initially and $B$ is moving with velocity $v$ along x-axis. After collision $B$ has a velocity $\cfrac{v}{2}$ in a direction perpendicular to the original direction. The mass $A$ moves after collision in the direction

physics momentum collision of two rigid bodies energy and collisions understanding collisions

  1. Same as that of $B$

  2. Opposite to that of $B$

  3. $\theta=\tan^{-1}{(1/2)}$ to the x-axis

  4. $\theta=\tan^{-1}{(-1/2)}$ to the x-axis

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Correct Option: A

A rod of length on two metal pads of same height from a height $h$. The coefficients of restitution of the metal pads are ${e} _{1}$ and ${e} _{2}$ (${e} _{1}> {e} _{2}$). The angular velocity of the rod after it recoils is

physics momentum collision of two rigid bodies energy and collisions understanding collisions

  1. $\cfrac { { e } _{ 1 } }{ { e } _{ 2 } } l\sqrt { 2gh } $

  2. $\cfrac { { e } _{ 1 }-{ e } _{ 2 } }{ l } \sqrt { 2gh } $

  3. $\cfrac { { e } _{ 1 }+1 }{ { e } _{ 2 }+1 } \sqrt { 2gh } $

  4. $\cfrac { { e } _{ 1 }+1 }{ { e } _{ 2 }-1 } \sqrt { 2gh } $

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Correct Option: C

In a collision between two solid spheres. velocity of separation along the line of impact (assume no external forces act on the system of two spheres during impact):

physics momentum collision of two rigid bodies energy and collisions understanding collisions

  1. Cannot be greater than velocity of approach

  2. Cannot be less than velocity of approach

  3. Cannot be equal to velocity of approach

  4. none of these

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Correct Option: A
Explanation:

$\begin{array}{l} e=\dfrac { { volume\, \, of\, \, sep } }{ { volume\, \, of\, \, app } }  \ 0<e<1 \ \Rightarrow Volume\, \, \, of\, \, sep<volume\, \, of\, \, app \end{array}$

$\therefore $ Option $A$ is correct.

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

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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. $0.8$

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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