The distances of two satellites from the surface of the earth are R and 7 R. Their time periods of rotation are in the ratio

Question

The distances of two satellites from the surface of the earth are R and 7 R. Their time periods of rotation are in the ratio (A) 1: 7 (B) 1: 8 (C) 1: 49 (D) 1: 73 / 2

Tardigrade Admin · Accepted Answer

As T2 propto r3, where r= distance from the centre of the earth. ∴ (T1/T2)=((r1/r2))3 / 2 Here, r1=2 R, r2=8 R ∴ (T1/T2)=((2 R/8 R))3 / 2=(1/43 / 2)=(1/8)

Q. The distances of two satellites from the surface of the earth are $R$ and $7 R$ . Their time periods of rotation are in the ratio

1 : 7

1 : 8

1 : 49

$1 : 7^{3/2}$

As $T^{2} \propto r^{3}$ ,
where $r =$ distance from the centre of the earth.
$∴ \frac{T _{1}}{T _{2}} = (\frac{r _{1}}{r _{2}})^{3/2}$
Here, $r_{1} = 2 R, r_{2} = 8 R$
$∴ \frac{T _{1}}{T _{2}} = (\frac{2 R}{8 R})^{3/2} = \frac{1}{4 ^{3/2}} = \frac{1}{8}$

Q. The distances of two satellites from the surface of the earth are R and 7R. Their time periods of rotation are in the ratio