Tag: work, energy and power

Quizzes (16) Questions (235)

Questions Related to work, energy and power

Multiple choice modelling collisions collisions momentum work, energy and power physics

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 

  1. 1 : e

  2. e : 1
  3. $1 : e^3$
  4. $e^2 : 1 $
Reveal answer Fill a bubble to check yourself
D Correct answer
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$

Multiple choice modelling collisions collisions momentum work, energy and power physics

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 

  1. $30 ^ { \circ }$
  2. $60 ^ { \circ }$
  3. $90 ^ { \circ }$
  4. $120 ^ { \circ }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a perfectly inelastic collision of equal masses m, m*v1 + m*v2 = 2*m*v_final. If v_final = v/2, then v1 + v2 = v. This implies the angle between the initial velocity vectors must be 90 degrees.

Multiple choice modelling collisions collisions momentum work, energy and power physics

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?

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Nothing is mentioned about coefficient of restitution. 

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

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

Geothermal energy is feasible in regions that

  1. Are near the sea

  2. Have thermal plants

  3. Have coal mines

  4. Are over hot spots in the crust
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Geothermal energy relies on heat from the Earth's interior. Regions over hot spots in the crust, where magma is relatively close to the surface, are ideal for tapping into this heat.

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

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:

  1. $2.3\ ms^{-1}$
  2. $4.6\ ms^{-1}$
  3. $9.2\ ms^{-1}$
  4. $6\ ms^{-1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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} $

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


$v = |\vec {v}| = \sqrt {1 + 4 + 16} = 4.6\ ms^{-1}$.
Multiple choice collisions in one dimension collisions work, energy and power mechanics physics

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:

  1. $30\ ms^{-1}$
  2. $40\ ms^{-1}$
  3. $50\ ms^{-1}$
  4. $60\ ms^{-1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation


As momentum is conserved, we can say,

$m(v-10)=mv _2$

$v _2=(v-10)$

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

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

$0.6v+6=v-10$

$0.4v=16$ 

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

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

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:

  1. $\cfrac{1}{2}m{v}^{2}$
  2. $m{v}^{2}$
  3. $\cfrac{3}{2}m{v}^{2}$
  4. $\cfrac{5}{2}m{v}^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By conservation of momentum, the initial momentum is zero, so the vector sum of the momenta of the three pieces must also be zero. Two pieces of mass m move at speed v in perpendicular directions, giving a combined momentum magnitude of m*v*sqrt(2). The third piece of mass 2m must balance this, having momentum 2m*v_3 = m*v*sqrt(2), so v_3 = v/sqrt(2). Summing the kinetic energies of all three pieces gives KE = (1/2)m*v^2 + (1/2)m*v^2 + (1/2)(2m)(v/sqrt(2))^2 = (3/2)m*v^2.

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

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)${ u } _{ 1 }-{ v } _{ 1 }={ v } _{ 2 }+{ u } _{ 2 }$

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a 1D elastic collision between particles of equal mass, the particles simply exchange velocities. Thus, v1 = u2 and v2 = u1. Equation A (u1 + v1 = v2 + u2) becomes u1 + u2 = u1 + u2, which is correct. Equation B (u1 - v1 = v2 + u2) becomes u1 - u2 = u1 + u2, which is incorrect unless u2 = 0.