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JEE Main 202226 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
26 June
Shift
Evening Shift
Subject
Physics
Chapter
Waves and Sound

JEE Main 2022 · 26 June · Evening Shift · Physics · Waves and Sound

For a specific wavelength 670nm of light coming from a galaxy...

For a specific wavelength 670nm670nm of light coming from a galaxy moving with velocity vv, the observed wavelength is 670.7nm670 . 7nm. The value of vv is

Options

  1. A3×108ms−13 \times {10}^{8}{ms}^{- 1}
  2. B3.13×105ms−13 . 13 \times {10}^{5}{ms}^{- 1}
  3. C3×1010ms−13 \times {10}^{10}{ms}^{- 1}
  4. D4.48×105ms−14 . 48 \times {10}^{5}{ms}^{- 1}

Correct answer

B. 3.13×105ms−13 . 13 \times {10}^{5}{ms}^{- 1}

Step-by-step solution

The apparent change in the wavelength is given by

Δλλ=vc\dfrac{\Delta\lambda}{\lambda} = \dfrac{v}{c}

⇒v=cΔλλ=3×108×(670.7−670)670=3.13×105ms−1⇒ v = c\dfrac{\Delta\lambda}{\lambda} = \dfrac{3 \times {10}^{8} \times \left(670 . 7 - 670\right)}{670} = 3 . 13 \times {10}^{5}m{s}^{- 1}

Hence, velocity of the planet is 3.13×105ms−13 . 13 \times {10}^{5}m{s}^{- 1}.

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