InterviewSolution
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InterviewSolution
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A uniform stick of length `l` is mounted so as to rotate about a horizontal axis perpendicular to the stick and at a distance `d` from the centre of mass. The time period of small oscillation has a minimum value when `d//l` isA. `(1)/(sqrt(2)`B. `(1)/sqrt(12)`C. `(1)/sqrt(3)`D. `(1)/sqrt (6)` |
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Answer» Correct Answer - B `T = 2pi sqrt((I)/(mgd))` `= 2pi sqrt((ml^(2))/(12) + md^(2))/(mgd)` `= 2pi sqrt ((l^(2) + 12d^(2))/(12d))` `= 2pi sqrt (((l^(2))/(12d) + d))` `T` is minimum when first derivation of the quantity inside the root with respect to `d` is zero. `- (l^(2))/(12d^(2)) + 1 = 0` or `(d)/(l) = (1)/sqrt (12)` |
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