Question

The apparent wavelength of light from a star moving away from the earth is $0.01\%$ more than its real wavelength. The velocity of star is:

• A. $60km/sec$
• B. $15km/sec$
• C. $150km/sec$
• D. $30km/sec$

Answer 1

The correct option is D $30km/sec$

Given that,

Wavelength of light coming from the earth $=\lambda$

Wavelength of light coming from the distant star,$\Delta \lambda =\lambda +\lambda \left(\frac{0.01}{100}\right)$

Now,

$\Delta \lambda ={\lambda }^{\prime }-\lambda$

$\Delta \lambda =\lambda +\lambda \left(\frac{0.01}{100}\right)-\lambda$

$\Delta \lambda =\lambda \left(\frac{0.01}{100}\right)$

$\frac{\Delta \lambda }{\lambda }=\frac{v}{c}$

$v=3\times {10}^8\times {10}^{-4}$

$v=30km/s$

Hence, the velocity of star is $30km/s$