Tag: work, energy and power

Questions Related to work, energy and power

A body dropped freely from a height h on to a horizontal plane, bounces up and down and finally comes to rest.The coefficient of restitution is e. The ratio of velocities at the beginning and after two rebounds is 

modelling collisions collisions momentum work, energy and power physics

  1. 1 : e

  2. e : 1

  3. $1 : e^3$

  4. $e^2 : 1 $

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Correct Option: D
Explanation:

Let initial velocity is v at time of collision. $v = \sqrt { 2gh } $

after first re bound velocity ${v} _{1} = ev$
after second rebound velocity ${v} _{2} = e{v} _{1} = {e}^{2}v$
ratio $=\dfrac { { v } _{ 2 } }{ v } =\dfrac { { e }^{ 2 }v }{ v } $
$ ={ e }^{ 2 }:1$

Two bodies of equal masses moving with equal speeds makes a perfectly inelastic collision. If the speed after the collision is reduced to half, the velocities of approach is 

modelling collisions collisions momentum work, energy and power physics

  1. $30 ^ { \circ }$

  2. $60 ^ { \circ }$

  3. $90 ^ { \circ }$

  4. $120 ^ { \circ }$

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Correct Option: C

Two small spheres of equal mass, and heading towards each other with equal speeds, undergo a headon collision (no external force acts on system of two spheres). Then which of the following statement is correct?

modelling collisions collisions momentum work, energy and power physics

  1. Their final velocities must be zero

  2. Their final velocities may be zero

  3. Each must have a final velocity equal to the others initial velocity

  4. Their velocities must be reduced in magnitude

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Correct Option: B
Explanation:

Nothing is mentioned about coefficient of restitution. 

Hence the only true statement is 'their final velocities may be zero.'

The moving striker of the carom board will possess------ energy

physics work, energy and power forms of energy and energy conservation energy for everything forms of energy

  1. Kinetic

  2. Potential

  3. Solar

  4. Electric

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Correct Option: A
Explanation:

as the striker is moving it will possess kinetic enegry

Geothermal energy is feasible in regions that

physics work, energy and power forms of energy and energy conservation energy for everything forms of energy

  1. Are near the sea

  2. Have thermal plants

  3. Have coal mines

  4. Are over hot spots in the crust

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Correct Option: D

A particle of mass $1\ g$ moving with a velocity $\vec {v _{1}} = 3\hat {i} - 2\hat {j} ms^{-1}$ experiences a perfectly in elastic collision with another particle of mass $2\ g$ and velocity $\vec {v _{2}} = 4\hat {j} - 6\hat {k} ms^{-1}$. The velocity of the particle is:

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

  1. $2.3\ ms^{-1}$

  2. $4.6\ ms^{-1}$

  3. $9.2\ ms^{-1}$

  4. $6\ ms^{-1}$

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Correct Option: B
Explanation:

From conservation of momentum
$m _{1}\vec {v _{1}} + m _{2}\vec {v _{2}} = (m _{1} + m _{2})\vec {v}$


$1\times (3\hat {i} - 2\hat {j}) + 2\times (4\hat {j} - 6\hat {k}) = (1 + 2)\vec {v}$

$\Rightarrow 3\hat {i} + 6\hat {j} - 12\hat {k} = 3\vec {v} $

$\Rightarrow \vec {v} = \hat {i} + 2\hat {j} - 4\hat {k}$


$v = |\vec {v}| = \sqrt {1 + 4 + 16} = 4.6\ ms^{-1}$.

A ball P moving with a speed of $v \ ms^{-1}$ collides directly with another identical ball Q moving with a speed $10\ ms^{-1}$ in the opposite direction. P comes to rest after the collision. If the coefficient of restitution is 0.6, the value of $v$ is:

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

  1. $30\ ms^{-1}$

  2. $40\ ms^{-1}$

  3. $50\ ms^{-1}$

  4. $60\ ms^{-1}$

Show answer
Correct Option: B
Explanation:


As momentum is conserved, we can say,

$m(v-10)=mv _2$

$v _2=(v-10)$

$e=\dfrac{v _2-v _1}{u _1+u _2}=\dfrac{(v-10)-0}{(v+10)}$

$0.6=\dfrac{v-10}{v+10}$

$0.6v+6=v-10$

$0.4v=16$ 

$v=40\ ms^{-1}$

A ball is dropped from a $45\ m$ high tower while another is simultaneously thrown upward from the foot at $20\ m/s$, along the same vertical line. If the collision is perfectly elastic, first ball reaches ground after time-

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

  1. $2s$

  2. $3s$

  3. $4s$

  4. $5s$

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Correct Option: A

A body of mass $4m$ at rest explodes into three pieces. Two of the pieces each of mass $m$ move with a speed $v$ each in mutually perpendicular directions. The total kinetic energy released is:

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

  1. $\cfrac{1}{2}m{v}^{2}$

  2. $m{v}^{2}$

  3. $\cfrac{3}{2}m{v}^{2}$

  4. $\cfrac{5}{2}m{v}^{2}$

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Correct Option: A

A particle of mass m moving with velocity ${u} _{1}$ collides elastically with particle of same mass moving with velocity ${u} _{2}$ in the same direction. After collision their speeds are ${v} _{1}$ and ${v} _{2}$ respectively then-
(A) ${ u } _{ 1 }+{ v } _{ 1 }={ v } _{ 2 }+{ u } _{ 2 }$
(B)${ u } _{ 1 }-{ v } _{ 1 }={ v } _{ 2 }+{ u } _{ 2 }$

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

  1. Both the equations A and B are correct

  2. Both the equations A and B are incorrect

  3. Equation A is correct but not B

  4. Equation B is correct but not A

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Correct Option: C