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The density of the core a planet is rho(...

The density of the core a planet is `rho_(1)` and that of the outer shell is `rho_(2)`. The radii of the core and that of the planet are `R` and `2R` respectively. The acceleration due to gravity at the surface of the planet is same as at a depth `R`. Find the ratio of `(rho_(1))/(rho_(2))`

A

2.3

B

4.5

C

3.2

D

5.4

Text Solution

Verified by Experts

The correct Answer is:
A
(a) `(Gm_(1))/(R^(2))=(G(m_(1)+m_(2)))/((2R)^(2))`
`4m_(1)=m_(1)+m_(2)`
`2m_(1)=m_(2)`
`3((4)/(3)piR^(3)rho_(1))=(4)/(3)pi[8R^(3)-R^(3)]rho_(2)`
`3rho_(1)=7rho_(2)`
`(rho_(1))/(rho_(2))=(7)/(3)=2.3`
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