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  • A rocket is going towards moon with a speed v. The astronaut in the rocket sends signals of frequency v towards the moon and receives them back on reflection from the moon. What will be the fr

A rocket is going towards moon with a speed v. The astronaut in the rocket sends signals of frequency v towards the moon and receives them back on reflection from the moon. What will be the frequency of the signal received by the astronaut \mathrm{(Take \, \, v<<c )}

Option: 1

\mathrm{\frac{c}{c-v} v}


Option: 2

\mathrm{\frac{c}{c-2 v} v}


Option: 3

\mathrm{\frac{2 v}{c} v}


Option: 4

\mathrm{\frac{2 c}{v} v}


Answers (1)

best_answer

In this case, we can assume as if both the source and the observer are moving towards each other with speed v.

Hence  \mathrm{v^{\prime}=\frac{\mathrm{c}-\mathrm{u}_{\mathrm{o}}}{\mathrm{c}-\mathrm{u}_{\mathrm{s}}} v=\frac{\mathrm{c}-(-\mathrm{v})}{\mathrm{c}-\mathrm{v}} v=\frac{\mathrm{c}+\mathrm{v}}{\mathrm{c}-\mathrm{v}} v}

\mathrm{ =\frac{(c+v)(c-v)}{(c-v)^2} v=\frac{c^2-v^2}{c^2+v^2-2 v c} v }
Since \mathrm{v<<c, therefore \, v^{\prime}=\frac{c^2}{c^2-2 v c}=\frac{c}{c-2 v} v}

Posted by

jitender.kumar

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