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If two planets of radii R(1) and R(2) ha...

If two planets of radii `R_(1) and R_(2)` have densities `d_(1) and d_(2)`, then the ratio of their respective acceleration due to gravity is

A

`R_(1)d_(1):R_(2)d_(2)`

B

`R_(1)^(2)d_(1):R_(2)^(2)d_(2)`

C

`R_(1)^(3)d_(1):R_(2)^(3)d_(2)`

D

`R_(1)d_(1)^(2):R_(2)^(2)d_(2)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
We know the gravity, `g = (4)/(3)pi GRd`
Here given densities `d_(1) and d_(2)` and radii `R_(1) and R_(2)`
So, `(g_(1))/(g_(2))=((4)/(3)piGR_(1)d_(1))/((4)/(3)piGP_(2)d_(2))rArr(g_(1))/(g_(2))=(R_(1)d_(1))/(R_(2)d_(2))`.
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Knowledge Check

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