The wavelength of light received from a galaxy is 10% greater than that received from identical source on the earth. The velocity of the galaxy relative to the earth is

Options

A. A) `3xx 10^(8) ms^(-1)`
B. B) `3xx 10^(7) ms^(-1)`
C. C) `3xx 10^(6) ms^(-1)`
D. D) `3xx 10^(5) ms^(-1)`

Answer

To solve the problem, we need to find the velocity of the galaxy relative to the Earth based on the change in wavelength of light received from it. Here’s a step-by-step solution:

### Step 1: Understand the Given Information
We are given that the wavelength of light received from a galaxy is 10% greater than that received from an identical source on Earth. This means:
- If the original wavelength (λ) is received from Earth, the wavelength from the galaxy (λ') can be expressed as:
\[ \lambda' = \lambda + 0.1\lambda = 1.1\lambda \]

### Step 2: Calculate the Change in Wavelength
The change in wavelength (Δλ) is given by:
\[ \Delta \lambda = \lambda' - \lambda = 1.1\lambda - \lambda = 0.1\lambda \]

### Step 3: Use the Formula for Velocity
We can relate the change in wavelength to the velocity of the galaxy using the formula:
\[ V = \frac{\Delta \lambda}{\lambda} \cdot c \]
where:
- \( V \) is the velocity of the galaxy relative to Earth,
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) m/s).

### Step 4: Substitute the Values
From the previous steps, we have:
\[ \frac{\Delta \lambda}{\lambda} = 0.1 \]
Substituting this into the velocity formula gives:
\[ V = 0.1 \cdot c = 0.1 \cdot (3 \times 10^8 \text{ m/s}) \]

### Step 5: Calculate the Velocity
Now, calculate the velocity:
\[ V = 0.1 \cdot 3 \times 10^8 = 3 \times 10^7 \text{ m/s} \]

### Step 6: Identify the Correct Option
The calculated velocity \( V = 3 \times 10^7 \text{ m/s} \) corresponds to option B.

### Final Answer
The velocity of the galaxy relative to the Earth is:
\[ \boxed{3 \times 10^7 \text{ m/s}} \]

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