Question

The Jupiter's period of revolution around the Sun is $12$ times that of the Earth. Find the ratio gravitational force exerted on Earth to that on Jupiter

• A. $27.47$
• B. $\frac{1}{27.47}$
• C. $16.2$
• D. $\frac{1}{16.2}$

Answer 1

The correct option is A $27.47$

$T_{earth}=2\pi {\left(\frac{R_e^3}{G{M}_S}\right)}^{0.5}$
$T_{jupiter}=2\pi {\left(\frac{R_j^3}{G{M}_S}\right)}^{0.5}$
Given ratio, $\frac{T_j}{T_e}=12$
$\Rightarrow 2\pi {\left(\frac{R_j^3}{G{M}_S}\right)}^{0.5}\times {\left(\frac{G{M}_S}{R_e^3}\right)}^{0.5}\times \frac{1}{2\pi }=12$

So, $\frac{R_j}{R_e}={12}^{0.67}$

$GravitationalforceF\propto \frac{1}{R}$

$\Rightarrow \frac{F_e}{F_j}={\left(\frac{R_j}{R_e}\right)}^2={12}^{\frac{4}{3}}=27.47$