JEE Main201815 Apr 2018Morning ShiftPhysicsGravitationActual
Take the mean distance of the moon and the sun from the earth to be 0.4 10^6 ~km and 150 10^6 ~km respectively. Their masses are 8 10²² ~kg and 2 10³⁰ ~kg respectively. The radius of the earth is 6400 ~km . Let F₁ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and F ₂ be the difference in the force exerted by the sun at the nearest and farthest points on the earth.
Options
- A2
- B6
- C10⁻²
- D0.6
Correct answer
A. 2
Step-by-step solution
As we know, Gravitational force of attraction, F = GMm R ^2 ~F ₁= GM _ e m r ₁^2 and F ₂= GM _ e M _ s r ₂^2 F ₁= 2 GM _ e m r ₁^3 r ₁ and F ₂= GM _ e M _ s r ₂^3 r ₂ Using r ₁= r ₂=2 R _ earth ; m =8 10²² ~kg ; M _ s =2 10³⁰ ~kg r ₁=0.4 10^6 ~km ^2 and r ₂=150 10^6 ~km F ₁ F ₂ = ( 8 10²² 2 10³⁰ ) ( 150 10^6 0.4 10^6 )^3 1 2