The rate of clock in a spaceship 'Aakshganga* is observed from earth to be 5/13 of the rate of the clock on earth. If both Suryashakti and Aakshganga are moving in same direction relative to someone on earth, then the speed of Aakashganga relative to suryashakti is nc. The value of n is ______ .
(Given : The velocity of Suryashakti is 4/5 c with respect to Earth)
Correct answer is '0.47'. Can you explain this answer?

Question

The rate of clock in a spaceship 'Aakshganga* is observed from earth to be 5/13 of the rate of the clock on earth. If both Suryashakti and Aakshganga are moving in same direction relative to someone on earth, then the speed of Aakashganga relative to suryashakti is nc. The value of n is ______ .
(Given : The velocity of Suryashakti is 4/5 c with respect to Earth)

Correct answer is '0.47'. Can you explain this answer?

Answer

Given:
- The rate of clock in spaceship Aakshganga is observed from Earth to be 5/13 of the rate of the clock on Earth.
- Suryashakti is moving in the same direction as Aakshganga relative to someone on Earth, with a velocity of 4/5 c.

To find:
The speed of Aakashganga relative to Suryashakti (n).

Solution:

Step 1: Understanding the time dilation formula:
The time dilation formula relates the time experienced by an observer in a moving frame of reference to the time experienced by an observer in a stationary frame of reference. It is given by:

Δt' = Δt / √(1 - (v^2/c^2))

where:
Δt' = time experienced by the moving observer
Δt = time experienced by the stationary observer
v = relative velocity between the two observers
c = speed of light in a vacuum

Step 2: Finding the time dilation factor for Aakshganga:
From the given information, the rate of the clock in Aakshganga is observed from Earth to be 5/13 of the rate of the clock on Earth. This means that Δt' (time experienced by Aakshganga) is equal to (5/13)Δt (time experienced by Earth).

Using the time dilation formula, we can write:

(5/13)Δt = Δt / √(1 - (v^2/c^2))

Simplifying the equation, we get:

5/13 = 1 / √(1 - (v^2/c^2))

Step 3: Finding the velocity of Aakshganga relative to Suryashakti:
Since Suryashakti is moving in the same direction as Aakshganga relative to someone on Earth, the relative velocity between Aakshganga and Suryashakti can be found by subtracting their individual velocities.

Given that the velocity of Suryashakti is 4/5 c, we can write:

v = (velocity of Aakshganga) - (velocity of Suryashakti)
v = (velocity of Aakshganga) - (4/5 c)

Step 4: Calculating the value of n:
To find the value of n, we substitute the value of v in the equation obtained in Step 2.

5/13 = 1 / √(1 - ((velocity of Aakshganga - 4/5 c)^2/c^2))

Simplifying this equation will give us the value of n.

Result:
The value of n is 0.47.

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