InterviewSolution
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InterviewSolution
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A stone of mass 1 kg tied to a light inextensible string of lenth `L=(10)/(3)m`, whirling in a circular path in a vertical plane. The ratio of maximum tension to the minimum tension in the string is 4. If g is taken to be `10ms^(-2)`, the speed of the stone at the highest point of the circle isA. `20 m//sec`B. `10 sqrt3 m//sec`C. `5 sqrt2 m//sec`D. `10 m//sec` |
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Answer» Correct Answer - D Since the maximum tension `T_(B)` in the string moving to the vertical circle is at the bottom and minimum tension `T_(T)` is at the top. `:. T_(B) = (mv_(B)^(2))/(L) + mg and T_(T) = (mv_(T)^(2))/(L) - mg` `:. (T_(B))/(T_(T)) = ((mv_(B)^(2))/(L) + mg)/((mv_(T)^(2))/(L) - mg) = (4)/(1) or (v_(B)^(2) + gL)/(v_(T)^(2) - gL) = (4)/(1)` or `v_(B)^(2) + gL = 4v_(T)^(2) - gL but v_(B)^(2) = v_(T)^(2) + 4gL` `:. v_(T)^(2) + 4gL+ gL = 4v_(T)^(2) - 4gL implies 3v_(T)^(2) = 9gL` `:. v_(T)^(2) = 3 xx gxx L = 3 xx 10 xx (10)/(3) or v_(T) = 10 m//sec` |
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