Question

The heavenly body is receding from earth, such that the fractional change in $\lambda$ is $1$, then its velocity is :

• A. $C$
• B. $\frac{3C}{5}$
• C. $\frac{C}{5}$
• D. $\frac{2C}{5}$

Answer 1

The correct option is A $C$

When a planet or stars are receding away from earth. If f is frequency of vibration.
Then, f = $\frac{c}{\lambda }$
If v = velocity of body moving away
${\lambda }^{\prime }$ = apparent wave length to an observer on the earth
${\lambda }^{\prime }$ = $\frac{(c+v)}{f}$ (c and v are in opposite to each other)
= $\left(\frac{c+v}{c}\right)\lambda$ ${\lambda }^{\prime }$= $(1+\frac{v}{c})\lambda$
$\frac{{\lambda }^{\prime }-\lambda }{\lambda }$ = $\frac{v}{c}$
Fractional change in wavelength
$\therefore 1$ = $\frac{v}{c}$ $\Rightarrow$ v = c