Tag: relativistic mechanics

Questions Related to relativistic mechanics

A girl runs a $100 m$ dash. Her dad cheers for her as he watches.
According to the special theory of relativity (although the effects would be very slight) which of the following statements could be accurately stated (because of the effects of special relativity)?

relativistic mechanics option a: relativity physics

  1. After the race, the dad could say to his daughter, "You were less massive during the race than you are now"

  2. After the race, the girl could say, "My time was a little better than I expected, but the race actually was not quite $100 m$ long

  3. During the race, the girl could yell to here dad, "You are less massive now than you were before the race!"

  4. After the race, the dad could say to his daughter, "During the race, you were taller than you are now"

  5. During the race, the girl could yell to her dad, "You are shorter than you were before the race"

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Correct Option: B
Explanation:
After the race, the girl could say, "My time was a little better than I expected, but the race actually was not quite 100m long, as Einstein's theory of special relativity states that the length of objects moving at relativistic speeds undergoes a contraction along the dimension of motion.

The dynamic mass of electron having rest mass $m _0 $ and moving with speed $0.8 c $ is :

relativistic mechanics option a: relativity physics

  1. $0.6 m _0 $

  2. $0.8 m _0 $

  3. $ \dfrac{5}{3} m _{o}$

  4. $ 1.25 m _0 $

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Correct Option: C
Explanation:

Mass of the moving electron is,

$m = \dfrac{{{m _0}}}{{\sqrt {\left( {1 - \frac{{{v^2}}}{{{c^2}}}} \right)} }}$

$ = \dfrac{{{m _0}}}{{\sqrt {\left( {1 - \frac{{{{\left( {0.8c} \right)}^2}}}{{{c^2}}}} \right)} }}$

$ = \dfrac{{{m _0}}}{{\sqrt {\left( {0.36} \right)} }}$

$ = \dfrac{{{m _0}}}{{0.6}}$

$ = \dfrac{{5{m _0}}}{3}$

Thus mass of the moving electron is $\dfrac{{5{m _0}}}{3}$.

When a material particle of rest mass $'m _0'$ attains the velocity of light, its mass becomes.

relativistic mechanics option a: relativity physics

  1. $0$

  2. $2m _0$

  3. $4m _0$

  4. Infinity

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Correct Option: D
Explanation:

Rest mass of an object is the inertial mass of that object when it is at rest. The relation between object's mass and rest mass is given by:  


$m = \dfrac{m _0}{\sqrt{1- \dfrac{v^2}{c^2}}}$

where $m _0$ is rest mass, $v$ is velocity of object and $c$ is speed of light. 
Now, if some particle attains the velocity of light then according to the equation mentioned above it's mass becomes infinity. 

Statement saying that energy is radiated or absorbed in discrete packets is given by ____________.

relativistic mechanics option a: relativity physics

  1. Planck

  2. Einstein

  3. Stephen

  4. Wien

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Correct Option: A
Explanation:
According to Planck’s quantum theory, Different atoms and molecules can emit or absorb energy in discreet quantities only. 

Quantum effects are important only when observing _____________.

relativistic mechanics option a: relativity physics

  1. small objects

  2. very large objects

  3. atomic size objects

  4. all of these

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Correct Option: C
Explanation:
Quantum theory is the theoretical basis of modern physics that explains the nature and behaviour of matter and energy on the atomic and subatomic level. So quantum effect is important only when observing atomic size objects.

The velocity of a particle is dependent on the times as $\upsilon =k(t-1)$ where $k=2\ m/s^{2}$. The distance covered in first three seconds will be

relativistic mechanics option a: relativity physics

  1. $18\ m$

  2. $5\ m$

  3. $3\ m$

  4. $6\ m$

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Correct Option: A

Special theory of relativity treats problems involving :

relativistic mechanics option a: relativity physics

  1. inertial frame of reference

  2. non-inertial frame of reference

  3. non-accelerated frame of reference

  4. accelerated frame of reference

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Correct Option: A
Explanation:
Einstein’s special theory of relativity is also based on two postulates, the constancy of the speed of electromagnetic radiation and the validity of physical laws in all inertial frame of reference

Behavior of matter on atomic level cannot be explained with ____________.

relativistic mechanics option a: relativity physics

  1. modern physics

  2. classical physics

  3. relativistic mechanics

  4. atomic spectra

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Correct Option: B
Explanation:
As Classical physics is the study of motion, projectiles, pulleys, and the planets. It mainly deals with the movement of large objects through space at a relatively low slow speed. 

According to special theory of relativity which one is not an absolute quantity?

relativistic mechanics option a: relativity physics

  1. time

  2. mass

  3. height

  4. both a and b

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Correct Option: D
Explanation:
According to classical physics time and mass are not an absolute quantity