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*Multiple options can be correct

QUESTION: 1

Consider two observers. One on the ground and another on a moving train. Both of them have clocks.

Choose the correct statements.

Solution:

From the rest frame of the ground observer the clock in the train is moving. The train clock runs slow from the point of view of the ground observer. From the rest frame of the train observer, the ground clock appears to be moving

∴ From the reference frame of the train, the ground clock runs slow

The correct answers are: The ground observer finds the train clock run slow., The train observer finds the ground clock run slow.

*Multiple options can be correct

QUESTION: 2

Which of the following statements is true?

Solution:

**Correct Answer :- a,d**

**Explanation :** b) mass of a photon is due to its momentum. When photon comes to rest velocity becomes zero thus mv=p=0. Hence rest mass of a photon is zero.

c) Rest mass (m0) 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 = m0/(1 - v^{2}/c^{2})^{1/2}

*Multiple options can be correct

QUESTION: 3

Choose the correct statement

Solution:

It is possible that neither obeys special theory of relativity but they can obey under some conditions.

*Multiple options can be correct

QUESTION: 4

Which of the following are lorentz transformations?

Solution:

In physics, the Lorentz transformations are a one-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity (the parameter) relative to the former. The respective inverse transformation is then parametrized by the negative of this velocity.

In the transformation for x and t, the coefficient of x and t, is the same!

The correct answer is:

*Multiple options can be correct

QUESTION: 5

In electrodynamics, the set of transformation rules for components of *E* and *B* are given as follows :

Here ' ~' denotes the components of *E* and *B* in a reference frame moving along the ** x**-axis with speed

Choose the correct statement.

Solution:

Consider the dot product

∴ *E*.*B* is relativistically in invariant

Consider the quantity

Now (1) – (2)

Invariant !

The correct answers are: is a relativistically invariant quantity, E^{2} - B^{2}c^{2 }is a relativistically invariant quantity

*Multiple options can be correct

QUESTION: 6

Tau leptons are observed to have an average half life of Δt_{1} in the frame *S*_{1} in which the leptons are at rest. In an inertial frame *S*_{2} which is moving at a speed *V*_{12} relative to *S*_{1}, the leptons are observed to have an average half life of Δt_{2}. In another inertial reference frame *S*_{3}, which is moving at a speed *V*_{13} relative to *S*_{1} and at a speed *V*_{23} relative to *S*_{2}, the leptons have an observed half life of Δt_{3}. Which of the following is true?

Solution:

** S_{1}** is at rest

∴ lifetime is least in this frame

The correct answers are:

*Multiple options can be correct

QUESTION: 7

According to Einsteins postulates of special theory of relativity

Solution:

The two postulates are:

The laws of physics are the same and can be stated in their simplest form in all inertial frames of reference.

The speed of light c is a constant, independent of the relative motion of the source.

To clarify the doubt:

The speed of light is a constant c = 3.00 × 10^{8} m/s in a vacuum. If you remember the effect of the index of refraction from The Law of Refraction, the speed of light is lower in matter.

*Multiple options can be correct

QUESTION: 8

The increased life times of the moving particles is a manifestation of

Solution:

Time dilation results in the clock of moving particle running slow increased life time.

The correct answer is: Time dilation

QUESTION: 9

Choose the correct statement

Solution:

Particles traveling at speeds close to the speed of light disintegrate slower than when they are at rest” is more apt when compared to “The life time of particles is greater when they are moving at speeds comparable to c

*Multiple options can be correct

QUESTION: 10

A rocket ship leaves earth at a speed of 3/5 c.When a clock on the rocket says 1 hour has elapsed, the rocket ship sends a light signal back to earth. Choose the correct statement (*s*)

Solution:

Rocket runs slow so earth clock reads

∴ Earth clock read 1 *hr* 15 minutes.

By the earth observer, the rocket is now at a distance of hours away.

∴

light signal will take 3/4 hour to return to earth.

Since, the signal left 5/4 hr after the departure

∴ light signal reaches 5/4 + 3/4 = 2hrs later.

Earth clock runs slow (in the reference frame of the rocket)

The correct answers are: According to the earth clock the signal was sent at 75 minutes after departure of the rocket, According to the rocket observer the signal reached earth 150 minutes after the rocket left., According to the earth clock, the signal reached earth 120 minutes after the rocket’s departure

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