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  • If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero, then the satellite will  Option: 1<

If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero, then the satellite will
 

Option: 1

continue to move in its orbit with same velocity
 


Option: 2

move tangentially to the original orbit in the same velocity
 


Option: 3

become stationary in its orbit
 


Option: 4

move towards the earth


Answers (1)

best_answer

Using Principle of conservation of energy

\mathrm{ -\frac{\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \mathrm{~m}\left(\frac{\mathrm{v}_{\mathrm{e}}}{\mathrm{r}}\right)^2=-\frac{\mathrm{GMm}}{\mathrm{R}+\mathrm{h}} }

\mathrm{ where \: v_{\mathrm{e}}=\sqrt{\frac{2 G M}{R}} }

\mathrm{ \text { or }-\frac{\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \frac{\mathrm{mv}_{\mathrm{e}}^2}{4}=-\frac{\mathrm{GMm}}{\mathrm{R}+\mathrm{h}} }

\mathrm{ \text { or } \frac{\mathrm{GMm}}{\mathrm{R}}+\frac{1}{8} \mathrm{~m}\left(\frac{2 \mathrm{GM}}{\mathrm{R}}\right)=-\frac{\mathrm{GMm}}{\mathrm{R}+\mathrm{h}} }

\mathrm{ \text { or }-\frac{1}{\mathrm{R}}+\frac{1}{4 \mathrm{R}}=-\frac{1}{\mathrm{R}+\mathrm{h}} \text { or }-\frac{3}{4 \mathrm{R}}=-\frac{1}{\mathrm{R}+\mathrm{h}} }

\mathrm{ \text { or }3R+3h=4R;h=\frac{R}{3} }

Hence option 4 is correct.






 

Posted by

Anam Khan

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