Tag: mechanics

Questions Related to mechanics

An object is moving towards a mirror with  a velocity v as shown in figure.if the collision between the mirror and the object is perfectly elastic, then the velocity of the image after collision with mirror in vector form is.

  1. $ - v\;\widehat j$

  2. $ - v\;\cos \;2\theta \widehat j + v\;\sin \;2\theta \;\widehat i$

  3. $ - v\widehat i$

  4. $ - v\;\cos \theta \;j - \;v\;\sin \theta \;\widehat i$


Correct Option: A

A body of mass $m$ moving with velocity $u$ collides elastically with another body of mass $m$ at rest. After collision, they moves in a plane with velocities $V _{1}$ and $V _{2}$ respectively. Then the angle beteen $\vec{V} _{1}$ and $\vec{V} _{2}$ is

  1. $zero$

  2. $60^{o}$

  3. $90^{o}$

  4. $180^{o}$


Correct Option: D

Two solid balls of rubber $A$ and $B$ whose masses are $200\ gm$ and $400\ gm$ respectively, are moving in mutually opposite directions. if the velocity of ball A is $0.3\ m/s$ and both the ball come to rest after collision, then the velocity of ball $B$ is :

  1. $0.15\ m/s$

  2. $-0.15\ m/s$

  3. $1.5\ m/s$

  4. $None\ of\ these$


Correct Option: B
Explanation:
Initial linear momentum of system 

$= [{{m} _{A}}{{\vec{v}} _{A}}+{{m} _{B}}{{\vec{v}} _{B}}]$

$= 0.2 \times  0.3 + 0.4 \times  vB$

Finally both balls come to rest \ final linear momentum = 0 

By the law of conservation of linear momenum        

$0.2 \times  0.3 + 0.4 \times  vB = 0$

$[{{v} _{B}}=-\dfrac{0.2\times 0.3}{0.4}=-0.15\ m/s]$

A ball of mass m moving with velocity V makes a head on  elastic collision with a ball of the same mass moving with velocity 2V towards it. Taking direction of V as positive velocities of the two balls after collision are

  1. -V and 2V

  2. 2V and -V

  3. V and -2V

  4. -2V and V


Correct Option: B

Two billiard balls undergo a head-on collision. Ball 1 is twice as heavy as ball 2. Initially, ball 1 moves with a speed $v$ toward ball $2$ which is at rest. Immediately after collision, ball 1 travels at a speed of $v/3$ in the same direction. What type of collision has occured?

  1. inelastic

  2. elastic

  3. completely inelastic

  4. cannot be determined from the information given


Correct Option: B
Explanation:

Solving the equation of conservation of momentum give us that the relative velocity of approach is equal to the relative velocity of separation. Hence coefficient of restitution is 1.
Which means collision is elastic. 

The collision of two balls of equal mass takes place at the origin of coordinates. Before collision, the components of velocities are $(V _x = 50 c m s^{-1},  V _{y} = 0)$ and $(V _{x} = -40 c m s^{-1}$ and $V _{y} = 30 c m s^{-1})$. The first ball comes to rest after collision. The velocity (components $V _{x}$ and $V _{y}$ respectively) of the second ball are

  1. 10 and 30 $c m s^{-1}$

  2. 30 and 10 $c m s^{-1}$

  3. 5 and 15 $c m s^{-1}$

  4. 15 and $5 c m s^{-1}$


Correct Option: C

Which of the following does not hold when two particles of masses $m _1$ and $m _2$ undergo elastic collision?

  1. When $m _1 =m _2$ and $m _2$ is stationary, there is maximum transfer of kinetic energy in head an collision

  2. When $m _1=m _2$ and $m _2$ is stationary , there is maximum transfer of momentum in head on collision

  3. when $m _1 >> m _2$ and $m _2$ is stationary, after head on collision $m _2$ moves with twice the velocity of $m _1$

  4. When the collision is oblique and $m _1=m _2$ with $m _2$ stationary, after the collision the particle move in opposite directions.


Correct Option: A

Two identical balls A and B collide head on elastically. If velocities of A and B, before the collision are +0.5 m/s and -0.3 m/s respectively, then their velocities, after the collision, are respectively

  1. -0.5 m/s and +0.3 m/s

  2. +0.5 m/s and +0.3 m/s

  3. +0.3 m/s and -0.5 m/s

  4. -0.3 m/s and +0.5 m/s


Correct Option: C
Explanation:

When identical balls collide $elastically $ they just $exchange$ their $SPEEDS$ and get reversed.

This can be verified by applying the $momentum$ conservation and $energy$ conservation, yes energy remains
 conserved for elastic collisions.
so the exchanged velocities will be following $v _1=0.3m/s$ and $v _2=-0.5m/s$

For head-on collision between two colliding balls of equal radii $r$, the impact parameter is equal to

  1. $2r$

  2. $Zero$

  3. $More \ than \ 2r$

  4. $Less\ than \ 2r$


Correct Option: A

In a one-dimensional collision between two particles, their relative velocity is $\bar{v _1}$ before the collision and $\bar{v _2}$ and the collision.

  1. $\bar{v _1} = \bar{v _2}$ if the collision is elastic.

  2. $\bar{v _1} = - \bar{v _2}$ if the collision is elastic.

  3. $|\bar{v _2}| = |\bar{v _1}|$ in all cases.

  4. $\bar{v _1} = - k \bar{v _2}$ in all cases, where k $\geq$ 1.


Correct Option: B,C,D
Explanation:

If $ { v } _{ 1 }$ is relative velocity before collision.
if ${ v } _{ 2 } $ is relative velocity before collision.
$e\le 1\$
$ e=\dfrac { { v } _{ 1 } }{ { -v } _{ 2 } } $


so $\left| { v } _{ 1 } \right| \ge \left| { v } _{ 2 } \right| $
also due to impact the ratios of velocity get changed,relative velocities D is correct. also, for elastic collision e$=$1.
So, option B is correct only if both particles have equal masses,not in general.