Tag: option a: relativity

Questions Related to option a: relativity

Radiation with energy that is easily detected as quanta _______________.

relativistic mechanics option a: relativity physics

  1. $1$ eV

  2. $1$ KeV

  3. $1$ MeV

  4. $10^{-10}$ eV

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Correct Option: C

Two masses of 1g and 4g are moving with equal K.E. The ratio of the magnitude of their linear momentum is-

relativistic mechanics option a: relativity physics

  1. 1 : 1

  2. 1 : 2

  3. 1 : 3

  4. 1 : 4

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Correct Option: B

Length contraction happens only __________________.

relativistic mechanics option a: relativity physics

  1. perpendicular to direction of motion

  2. along direction of motion

  3. both a and b

  4. none of these

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Correct Option: B

If a constant force acts on a particle, its acceleration will

relativistic mechanics option a: relativity physics

  1. remain constant

  2. gradually decrease

  3. gradually increase

  4. be undefined

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Correct Option: A
Explanation:
Acceleration happens because there is force applied to the object, if the force is constant, we have constant acceleration.

As the speed of a particle increases, its rest mass

relativistic mechanics option a: relativity physics

  1. increases

  2. decreases

  3. remains the same

  4. changes

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Correct Option: C
Explanation:

Rest mass $(m _o)$ is defined as the mass of the object at rest (or in rest frame) which remains constant.

Only the mass of the moving object changes as the speed increases  via   $m  = \dfrac{m _o}{\sqrt{1-\dfrac{v^2}{c^2}}}$
Hence option C is correct.

If $M$ and $m$ are moving mass and rest mass respectively of a body and $c$ is speed of light,

then kinetic energy of body is given by :

relativistic mechanics option a: relativity physics

  1. $K = [m - M]c^2$

  2. $K = [M - m]c^2$

  3. $K = Mc^2$

  4. $K = mc^2$

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Correct Option: B

A person is watching a rocket with an astronaut inside move by at a speed near the speed of light.
Which of the following statements is true?

relativistic mechanics option a: relativity physics

  1. The mass of the rocket is greater from the person's perspective than from the astronaut's perspective

  2. The mass of the rocket is the same from the perspective of the person and the astronaut

  3. The mass of the rocket is greater from the perspective of the astronaut than from the perspective of the person

  4. The person's mass is greater, from his own perspective, as the rocket flies by, than it was before the rocket flew by

  5. The astronaut's mass is greater, from his own perspective, as he flies by the person, than it was before he flew by the person

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Correct Option: A
Explanation:

Mass of the moving object as seen by the person in rest frame,  $m = \dfrac{m _o}{\sqrt{1-v^2/c^2}}$  $\implies m>m _o$

where  $m _o$ is the rest mass as seen by the astronaut in moving frame. 
Thus mass of rocket would be greater from the person's perspective than from the astronaut's perspective.

A man flies past a woman at a speed near the speed of light. What might correctly be said by whom as the man flies by? Assume that neither the man nor the woman usually travels so fast relative to other near-by objects

relativistic mechanics option a: relativity physics

  1. The man could say, "I am more massive than usual"

  2. The man could say, "Time is passing more slowly for me the usual"

  3. The woman could say to the man, "You are more massive than usual"

  4. The woman could say to the man, " You are wider than usual"

  5. The woman could say, "Time is passing more quickly for me than usual"

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Correct Option: C
Explanation:

Mass of the moving man as seen by the woman in rest frame           $m = \dfrac{m _o}{\sqrt{1-v^2/c^2}}$      $\implies m>m _o$

where  $m _o$ is the rest mass of the man. 
Thus according to the woman, the man seems to be more massive than usual.

When a rod moves at a relativistic speed v, its mass

relativistic mechanics option a: relativity physics

  1. must increase by a factor of $\gamma$

  2. may remain unchanged

  3. may increase by a factor other than $\gamma$

  4. may decrease

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Correct Option: A
Explanation:

Mass of moving object    $m  = \dfrac{m _o}{\sqrt{1 - \dfrac{v^2}{c^2}}}   = m _o \gamma$      where $m _o$ is the rest mass and  $\gamma  = \dfrac{1}{\sqrt{1- v^2/c^2}}$

Thus mass of the moving rod must increases by a factor of  $\gamma$.

By what fraction does the mass of a boy increase when he starts running at a speed of 12 km h$^{-1}$?

relativistic mechanics option a: relativity physics

  1. $11\times {10}^{-27}$

  2. $20\times {10}^{-27}$

  3. $6.17\times {10}^{-27}$

  4. $25.89\times {10}^{-27}$

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Correct Option: C
Explanation:

Given :   $v = 12$ km/h $ = 12\times \dfrac{5}{18}  =3.33$  m/s

Mass of the boy while running       $m  =\dfrac{m _o}{\sqrt{1 - (\frac{v^2}{c^2})^2}}$
$\therefore$  Fractional increase in the mass         $\dfrac{\Delta m}{m _o} = \dfrac{\dfrac{m _o}{\sqrt{1- (v/c)^2}} - m _o}{m _o}  = [1-(v/c)^2]^{-1/2} - 1$
$\implies $     $\dfrac{\Delta m}{m _o} = 1+ \dfrac{v^2}{2c^2}  -1  = \dfrac{v^2}{2c^2}$               (for $ v<< c$)

$\therefore$    $\dfrac{\Delta m}{m _o}  = \dfrac{3.33^2}{2 (3\times 10^8)^2}   =6.17\times 10^{-17}$  kg