The observed wavelength of light coming from a distant galaxy is found to be increased by $0.5 \%$ as compared with that coming from a terrestrial source. The galaxy is,

A star producing light of wavelength $6000 \stackrel{\circ }{\mathrm{A}}$ moves away from the earth with a speed of $5 \mathrm{km} {\mathrm{s}}^{-1}$. Due to Doppler effect, the shift in wavelength will be, $c=3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$,

A rocket is moving away from the earth at a speed of $6\times {10}^7 \mathrm{m} {\mathrm{s}}^{-1}$. The rocket has blue light in it. What will be the wavelength of light recorded by an observer on the earth? (Wavelength of blue light$=4600 \mathrm{\AA }$.)

A spectral line $\lambda=5000$ $\AA$ in the light coming from a distant star is observed as $5200 \mathrm{\AA }$. What will be recession velocity of the star?

A star moves away from earth at speed $0.8 \mathrm{c}$ while emitting light of frequency $6\times {10}^{14} \mathrm{Hz}$. What frequency will be observed on the earth in units of ${10}^{14} \mathrm{Hz} \text{? (}c=$ speed of light)

If the shift of wavelength of light emitted by a star is towards violet, then this shows that star is,

A star is moving away from the earth with a velocity of $100 \mathrm{km} {\mathrm{s}}^{-1}$. If the velocity of light is $3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$, then the shift of its spectral line of wavelength $5700 \mathrm{\AA }$ due to Doppler effect will be,

The velocity of a moving galaxy is $300 \mathrm{km} {\mathrm{s}}^{-1}$ and the apparent change in wavelength of a spectral line emitted from the galaxy is observed as $0.5 \mathrm{nm}$. Then, the actual wavelength of the spectral line is,