Tag: mechanics

Questions Related to mechanics

Choose the correct statements from the following :

collisions in one dimension collisions work, energy and power mechanics physics

  1. the general form of Newton's second law of motion is $\vec{F} _{ext} = \vec m a$.

  2. a body can have energy and get no momentum.

  3. a body having momentum must necessarily have kinetic energy.

  4. the relative velocity of two bodies in a head-on elastic collision remains unchanged in magnitude and direction.

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Correct Option: B,C
Explanation:

General form of 2nd law is $\vec { { F } _{ ext } } =m\vec { { a } _{ COM } } $
A body can have potential energy.
$KE=\dfrac { { p }^{ 2 } }{ 2m } $, so if a body has momentum it must have KE
its a fact that relative velocity in any type of collision changes in direction.

A point mass $M$ moving with a certain velocity collides with a stationary point mass $\dfrac{M}{2}$. The collision is elastic and one dimension. Let the ratio of the final velocities of $M$ and $\dfrac{M}{2}$ be $x$. The value of $x$ is :

collisions in one dimension collisions work, energy and power mechanics physics

  1. $2$

  2. $3$

  3. $\dfrac{1}{2}$

  4. $\dfrac{1}{4}$

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Correct Option: D
Explanation:

$v _1=\dfrac{\left(M-\dfrac{M}{2}\right)}{\left(M+\dfrac{M}{2}\right)}u _1=\dfrac{u _1}{3}$


$\therefore v _2=\dfrac{4u _1}{3}$


$\therefore \dfrac{v _1}{v _2}=\dfrac{1}{4}$

A body of mass $M$ moving with a speed $u$ has a head-on collision with a body of mass $m$ originally at rest. If $M>>m$, the speed of the body of mass $m$ after collision will be nearly:

collisions in one dimension collisions work, energy and power mechanics physics

  1. $\dfrac{um}{M}$

  2. $\dfrac{uM}{m}$

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

  4. $2u$

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Correct Option: D

A ball moving with a certain velocity hits another identical ball at rest. If the plane is frictionless and collision is elastic, the angle between the directions in which the balls move after collision, will be

collisions in one dimension collisions work, energy and power mechanics physics

  1. $30^{o}$

  2. $60^{o}$

  3. $90^{o}$

  4. $120^{o}$

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Correct Option: C

Two perfectly elastic objects $A$ and $B$ of identical mass are moving with velocities $15\ m/s$ and $10\ m/s$ respectively collide along the direction of line joining them. Their velocities after collision are respectively:

collisions in one dimension collisions work, energy and power mechanics physics

  1. $10\ m/s, 15\ m/s$

  2. $20\ m/s, 5\ m/s$

  3. $0\ m/s, 25\ m/s$

  4. $5\ m/s, 20\ m/s$

Show answer
Correct Option: A
Explanation:

$15m+10m=mv _1+mv _2$

$25=v _1+v _2$...............(i)
and $\dfrac{v _2-v _1}{u _1-u _2}=1$
$\Rightarrow \dfrac{v _2-v _1}{15-10}=1$
$\Rightarrow v _2-v _1=5$............(ii)
$v _1+v _2=25$
$\dfrac{v _2-v _1=5}{2v _2=30}$
$\therefore v _2=15m/s,v _1=10m/s$

A body of mass $8\ kg$ collides elastically with a stationary mass of $2\ kg$. If initial $KE$ of moving mass be $E$, the kinetic energy left with it after the collision will be:

collisions in one dimension collisions work, energy and power mechanics physics

  1. $0.80\ E$

  2. $0.64\ E$`

  3. $0.36\ E$

  4. $0.08\ E$

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Correct Option: C

If two bodies $A$ and $B$ of definite shape (dimensions of bodies are not ignored) $A$ is moving with speed of $10\ m/s$ and $B$ is in rest. They collide elastically. Then;

collisions in one dimension collisions work, energy and power mechanics physics

  1. body $A$ comes to rest and $B$ moves with speed of $10\ ms$

  2. they may move perpendicular to each other

  3. $A$ and $B$ may come to rest

  4. they must move perpendicular to each other

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Correct Option: B

A ball of mass $m$ moving with velocity $v$ collides elastically with another ball of identical mass coming from opposite direction with velocity $2v$. Their velocities after collision will be :

collisions in one dimension collisions work, energy and power mechanics physics

  1. $-v,2v$

  2. $-2v,v$

  3. $v,-2v$

  4. $2v,-v$

Show answer
Correct Option: B
Explanation:

$mv-2mv=mv _{1}+mv _{2}$
$-v=v _{1}+v _{2}$...........(1)

and $\dfrac{v _{2}-v _{1}}{v+2v}=1\Rightarrow v _{2}-v _{1}=3v$............(2)
Solving eqs. $(i)$ and $(ii)$,
$v _{2}-v _{1}=3v$
$\dfrac{v _{2}+v _{1}=-v}{2v _{2}=2v}$
$\therefore v _{2}=v$ and $-v _{1}=2v\therefore v _{1}=-2v$

Two solid rubber balls $A$ and $B$ having masses $200\ g$ and $400\ g$ respectively are moving in the opposite direction. A velocity of $A$ which is equal to $0.3\ m/s$. After the collision the two balls come to rest when the velocity of $B$ is 

collisions in one dimension collisions work, energy and power mechanics physics

  1. $0.15\ m/s$

  2. $1.5\ m/s$

  3. $-0.15\ m/s$

  4. $none\ of\ these$

Show answer
Correct Option: C
Explanation:

From conservation of linear momentum:

               $P _i=P _f$                  $(P _f=0)$

$m _{A}v _{A}+m _{B}v _{B}=0$
$v _{B}=-\dfrac{m _{A}v _{A}}{m _{B}}=-\dfrac{200\times 10^{-3}\times 0.3}{400\times 10^{-3}}$
$V _B=-\dfrac{60}{400}=-0.15$

A ball of mass $m _{1}$ is moving with velocity $v$. It collides head on elastically with a stationary ball of mass $m _{2}$. The velocity of ball becomes $\dfrac{v}{3}$ after collision, then the value of the ratio $\dfrac{m _{2}}{m _{1}}$ is:

collisions in one dimension collisions work, energy and power mechanics physics

  1. $1$

  2. $2$

  3. $3$

  4. $4$

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Correct Option: B