The masses of two planets are in the ratio `1 : 2`. Their radii are in the ratio `1 : 2`. The acceleration due to gravity on the planets are in the ratio

Options

A. `1:2`
B. `2:1`
C. `3:5`
D. `5:3`

Answer

B

Explanation

Acceleration due to gravity on eath is given by
`g=(GM)/(R^(2)) rarr g prop (M)/(R^(2))`
hence `(gP_(1))/(gp_(2))=(Mp_(1))/(Mp_(2))xx(R P_(2))/(RP_(1))^(2)`
substituting the given value in Eq I we get
`g_(p_(1))/(g_(p_(2))=1/2xx2/1^(2)=2/1 rarr gp_(1) : gp_(2)=2:1`