InterviewSolution
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InterviewSolution
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Pertaining to two planets, the ratio of escape velocities from respective surfaces is `1:2` , the ratio of the time period of the same simple pendulum at their respective surfaces is `2:1` (in same order). Then the ratio of their average densities isA. `1:1`B. `1:2`C. `1:4`D. `8:1` |
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Answer» Correct Answer - C Time period of simple pendulum, `T=2pi sqrt((l)/(g))or T prop (1)/(sqrt(g))` `(T_(1))/(T_(2))=sqrt((g_(2))/(g_(1)))=(2)/(1)rArr (g_(2))/(g_(1))=4`....(i) `v_(e)=sqrt(2gR)or v_(e)prop sqrt(gR)rArr (v_(e1))/(v_(e2))=sqrt((g_(1))/(g_(2)).(R_(1))/(R_(2)))=1:2` `:. sqrt((1)/(4)xx(R_(1))/(R_(2)))=(1)/(2)" "(because "from Eq. (i)" (g_(2))/(g_(1))=4)` `:. (R_(1))/(R_(2))=1` Further, `g=(Gm)/(R^(2))=(G((4)/(3)piR^(3)rho))/(R^(2))or g prop R rho` `:. (g_(1))/(g_(2))=(R_(1))/(R_(2)).(rho_(1))/(rho_(2))or((1)/(4))=(1)(rho_(1))/(rho_(2))or (rho_(1))/(rho_(2))=(1)/(4)`. |
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