Question

Two satellites of a planet have period $32$ days and $256$ days$.$ If the radius of the orbit of the former is $R,$ the orbital radius of the letter is

• A. $R/4$
• B. $2R$
• C. $4R$
• D. $R/2$

Answer 1

The correct option is B $2R$

Given,

$T_1=32days$

$T_2=256days$

$R_1=R$

$R_2=?$

The relation between the time period of satellite and the radius is

$T^2\propto R^3$

$\frac{T_2^2}{T_1^2}=\frac{R_2^3}{R_1^3}$

$R_2^3=R_1^3(\frac{T_2}{T_1}{)}^2$

$R_2^3=R^3(\frac{256}{32}{)}^2=8R^3$

$R_3^3=(2R{)}^3$

$R_2=2R$

The correct option is B.