A satellite $$A$$ of mass $$m$$ is at a distance of $$r$$ from the surface of the earth. Another satellite $$B$$ of mass $$2\,m$$ is at a distance of $$2\,r$$ from the earth’s centre. Their time periods are in the ratio of
A.
$$1:2$$
B.
$$1:16$$
C.
$$1:32$$
D.
$$1:2\sqrt 2 $$
Answer :
$$1:2\sqrt 2 $$
Solution :
Mass of satellite does not affect time period
$$\eqalign{
& \frac{{{T_A}}}{{{T_B}}} = {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^{\frac{3}{2}}} = {\left( {\frac{r}{{2r}}} \right)^{\frac{3}{2}}} = {\left( {\frac{1}{8}} \right)^{\frac{1}{2}}} = \frac{1}{{2\sqrt 2 }} \cr
& \therefore {T_A} = {T_B} = 1:2\sqrt 2 \cr} $$
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