InterviewSolution
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InterviewSolution
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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. `3/7`B. `9/4`C. `7/3`D. `3/8` |
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Answer» Correct Answer - C Let `m_(1)` be the mass of the core and `m_(2)` be the mass of outer shell. `g_(A)=g_(B)` (given) Then `(Gm_(1))/(R^(2))=(G(m_(1)+m_(2)))/((2R)^(2))` `:. 4m_(1)=(m_(1)+m_(2))` or `4{4/3piR^(2)rho_(1)}=4/3piR^(3)rho_(1)+{4/3pi(2R)^(3)-4/3piR^(3}rho_(2)` `:. 4rho_(1)=rho_(1)+7rho_(2)rArr (rho_(1))/(rho_(2))=7/3` |
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