Tag: work, energy and power

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Questions Related to work, energy and power

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

Two identical balls  $A$  and  $B$  having velocities of  $0.5\mathrm { m } / \mathrm { s }$  and  $- 0.3 \mathrm { m } / \mathrm { s }$  respectively collide elastically in one dimension. The velocities of  $B$  and  $\mathrm { A }$  after the collision respectively will be

  1. $0.3 \mathrm { m } / \mathrm { s } \text { and } 0.5 \mathrm { m } / \mathrm { s }$
  2. $- 0.5 \mathrm { m } / \mathrm { s } \text { and } 0.3 \mathrm { m } / \mathrm { s }$
  3. $0.5 \mathrm { m } / \mathrm { s } \text { and } - 0.3 \mathrm { m } / \mathrm { s }$
  4. $- 0.3 \mathrm { m } / \mathrm { s } \text { and } 0.5 \mathrm { m } / \mathrm { s }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When two identical masses collide elastically in one dimension, they simply exchange their velocities. Since A starts at 0.5 m/s and B at -0.3 m/s, after the collision, A will have -0.3 m/s and B will have 0.5 m/s.

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

A particle of mass $ m _1 $ hits another particle of mass $ m _2 $ at rest with a velocity $ \overrightarrow { u }  $. The collision is head-on and elastic.If $ m _1 >> m _2 $, then after collision, the velocity of $ m _2 $ will be-

  1. $ \overrightarrow { u } $
  2. $ - \overrightarrow { u } $
  3. $ 2 \overrightarrow { u } $
  4. $ -2 \overrightarrow { u } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a head-on elastic collision where a very massive body (m1) hits a stationary light body (m2), the velocity of the light body after the collision is twice the velocity of the incident massive body.

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

Which of the following does no 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 $ is stationary,there is minimum transfer of momentum in head on collision
  3. When $ m _1 >> 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.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice collisions in one dimension collisions work, energy and power mechanics physics

A perfectly elastic ball falls on a horizontal floor from a height in a time $t$. It will hit the floor again after a time $t'$. The ratio of $t'$ and t is 

  1. $1:1$
  2. $1:2$
  3. $2:1$
  4. $1:4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A ball falling freely from height h takes time t = sqrt(2h/g) to reach the floor. For a perfectly elastic collision, it rebounds with the same speed and takes the same time t to return to the original height. The total time elapsed before it hits the floor again is t' = 2t, making the ratio t' to t equal to 2:1.

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

A sphere P of mass m and  velocity $\underset{V _{1}}{\rightarrow}$  undergoes an oblique and perfectly elastic collision with an identical sphere Q initially at rest.  The  angle $\Theta $  between the velocites of the spheres after the collision shall be

  1. 0
  2. $45^{\circ}$
  3. $90^{\circ}$
  4. $180^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a perfectly elastic collision between two identical masses where one is initially at rest, the two bodies will move at an angle of 90 degrees to each other after the collision, provided the collision is oblique.

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

A neutron collides head-on with a stationary hydrogen atom $( _1H^1)$ in ground state, then choose the correct statement (assume that mass of neutron and mass of $( _1H^1)$ atom is same)

  1. If kinetic energy of the neutron is less than $13.6eV$, collision must be elastic
  2. If kinetic energy of the neutron is less than $13.6eV$, collision must be inelastic
  3. Inelastic collision may take place only when initial kinetic energy of neutron is greater than $13.6eV$

  4. Perfectly inelastic collisin cannot take place.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If the kinetic energy of the neutron is less than the excitation energy of the hydrogen atom (13.6 eV), the collision cannot result in internal energy changes, so it must be elastic to conserve energy and momentum.

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

Choose the correct statements from the following :

  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.
Reveal answer Fill a bubble to check yourself
B,C Correct answer
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.

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

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 :

  1. $2$
  2. $3$
  3. $\dfrac{1}{2}$
  4. $\dfrac{1}{4}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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


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


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

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

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:

  1. $\dfrac{um}{M}$
  2. $\dfrac{uM}{m}$
  3. $\dfrac{u}{2}$
  4. $2u$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When a very massive body (M) hits a stationary light body (m) head-on, the light body is projected forward with twice the velocity of the massive body.