Question

The wavelength of light observed on the earth from a moving star is found to decrease by $0.05$%. Relative to earth the star is

• A. Moving away with a velocity of $1.5\times {10}^{5}m/s$
• B. Moving away with a velocity of $1.5\times {10}^{4}m/s$
• C. Moving closer with a velocity of $1.5\times {10}^{5}m/s$
• D. Moving closer with a velocity of $1.5\times {10}^{4}m/s$

Answer 1

The correct option is C Moving closer with a velocity of $1.5\times {10}^{5}m/s$

By using the relation $\frac{\Delta \lambda }{\lambda }=\frac{a}{c},a=c\times \frac{\Delta \lambda }{\lambda }$
$=3\times {10}^8\times \frac{0.05}{1000}=1.5\times {10}^{5}m/s$
Also decrease in wavelength means the star is moving closer to the earth.