Question

The planet Jupiter is $5$ times farther from the sun than the earth, and the mass of Jupiter is $300$ times the mass of the earth. If $F_1$ is the gravitational force exerted by the sun on Jupiter, and $F_2$ is the gravitational force exerted by the sun on the earth, Find out the value of the ratio $\frac{F_1}{F_2}$?

• A. $\frac{1}{60}$
• B. $\frac{1}{12}$
• C. $8$
• D. $12$
• E. $60$

Answer 1

Answer: (D)

$12$

Let the distance between sun and the earth be $R$ and the mass of earth and sun be $M_e$ and $M_s$ respectively.

For earth : Gravitational force between earth and sun $F_2=\frac{G{M}_e{M}_s}{R^2}$

Mass of Jupiter $M_J=300M_e$

Distance between Jupiter and sun $R^{\prime }=5R$

$\therefore$ Gravitational force between jupiter and sun $F_1=\frac{G{M}_J{M}_s}{(R^{\prime }{)}^2}=\frac{G\left(300M_e\right)M_s}{25R^2}$

$⟹$ $\frac{F_1}{F_2}=\frac{G{M}_s\left(300M_e\right)/25R^2}{G{M}_s{M}_e/R^2}=\frac{300}{25}=12$