Take the mean distance of the moon and the sun from the earth to be`0.4 xx 10^(6) km` and `150 xx 10^(6) km` respectively. Their masses are `8 xx 10^(22) kg` and `2 xx 10^(30) kg` respectively. The radius of the earth of is `6400 km`. Let `DeltaF_(1)`be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and `DeltaF_(2)` be the difference in the force exerted b the sun at the nearest and farthest points on the earth. Then, the number closest to `(DeltaF_(1))/(DeltaF_(2))` is :

Options

A. 2
B. `10^(-2)`
C. `0.6`
D. 6

Answer

A

Explanation

`d_"me"=0.4xx10^(6)` km, `d_"se"=150xx10^6`km , `m_m=8xx10^22`kg `m_s=2xx10^30` kg `R_e=6.4xx10^6` m
`DeltaF_1=GMm_m[1/((d_"me"-R_e)^2)-1/((d_"me" + R_e )^2)]=(GMm_m)/(d_"me"4) xx(4d_"me" R_e)`
`DeltaF_2=(GMm_s)/(d_"se"4) xx(4d_"se"R_e). (DeltaF_1)/(DeltaF_2)=(m_m d_"se"^3)/(m_s d_"me"^3)=2`