If the ratio of the masses of two planets is 2 : 3 and the ratio of their radii are 4 : 7, then the inverse ratio of their accelerations due to gravity will be

Options

A. 49 : 24
B. 7 : 8
C. 24 : 49
D. 8 : 7

Answer

C

Explanation

`g_(1) = (GM_(1))/(R_(1)^(2))`
`g_(2) = (GM_(2))/(R_(2)^(2))`
`M_(1) : M_(2) = 2 : 3`,
`R_(1) : R_(2) = 4 : 7`
`(g_(1))/(g_(2))=(GM_(1))/(R_(1)^(2)) xx (R_(2)^(2))/(GM_(2))=(M_(1)R_(2)^(2))/(M_(2)R_(1)^(2))`
`= (2)/(3) xx (7^(2))/(4^(2))=(49 xx 2)/(3 xx 16)=(49)/(24)`
`therefore (g_(2))/(g_(1))=(24)/(49)`