InterviewSolution
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InterviewSolution
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A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constatn angular speed `omega`, as shown in the figure. At time t = 0, a small insect starts from O and moves with constant sped v, with respect to the rod towards the other end. It reaches the end of the rod at t =T and stops. The angular speed of the system remains `omega` throughout. The magnitude of the torque `(|vecpi|)` about O, as a function of time is best represented by which plot? A. B. C. D. |
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Answer» Correct Answer - B If `M` is mass of the rod, `l` is length of the rod, its moment of inertia about the end `O` of the rod `= Ml^(2)//3`.If `m` is mass of the insect and at any time `t`, the insect is at a distance `x` from `O`, its moment of inertia about `O = mx^(2)`. Therefore, moment of inertia of the system about `O` is `I = ((Ml^(2))/(3)+mx^(2))` Angular momentum of the system `L = I omega = ((Ml^(2))/(3)+mx^(2)) omega` Torque, `tau = (dL)/(dt) = (d)/(dt) ((Ml^(2))/(3)+mx^(2))omega` `= m omega (2x) (dx)/(dt) = 2m omega x. upsilon` But `x = upsilon t`. Therefore `tau = m omega (upsilon t) upsilon = 2 m omega upsilon^(2) t` Clearly, `tau prop t` At `t = T, upsilon = 0`. Therefore, `tau = 0`. Hence, the graph between `tau and t` is a stright line upto `t = T`. For `t gt T, tau = 0`. Choice (b) is correct. |
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