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
127.47
C
16.2
D
116.2

Solution

## The correct option is A $$27.47$$$$T_{earth} = 2\pi \left(\dfrac{R_e^3 }{GM_S}\right)^{0.5}$$$$T_{jupiter} = 2\pi \left(\dfrac{R_j^3 }{GM_S}\right)^{0.5}$$Given ratio, $$\dfrac{T_j}{T_e} = 12$$$$\Rightarrow 2\pi \left(\dfrac{R_j^3 }{GM_S}\right)^{0.5} \times \left(\dfrac{GM_S}{R_e^3 }\right)^{0.5} \times \dfrac{1}{2\pi}=12$$So, $$\dfrac{R_j}{R_e} = 12^{0.67}$$$$Gravitational\ force\ F \propto \dfrac{1}{R}$$$$\Rightarrow \dfrac{F_e}{F_j} = \left(\dfrac{R_j}{R_e}\right)^2 = 12^{\dfrac{4}{3}} = 27.47$$Physics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More