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Mechanical Properties Of Fluids

Question
CBSEENPH11019118

The wavelength of yellow sodium line (5896A) emitted by a star is red shifted to 6010 Å. What is the component of the star's recessional velocity along the line of sight? (For small recessional speeds, you may use a formula for Doppler effect analogous to that for sound). Speed of light is 30x108m/s.

Solution
Change in wavelength, because of red-shift, measured by observer (stationary) when the source moves away is given by,
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where,
 u is the velocity of the source.
Therefore,
Component of star's recessional velocity along the line of sight is,
 straight u equals straight c fraction numerator increment straight lambda over denominator straight lambda end fraction equals fraction numerator 6010 minus 5896 over denominator 5896 end fraction cross times 3 cross times 10 to the power of 8
                           almost equal to space 5.8 space cross times space 10 to the power of 6 space straight m divided by straight s