InterviewSolution
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InterviewSolution
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A person pulls along a rope wound up around a pulley with a constant force `F` for a time interval of `t` seconds. If `a` and `b` are the radii of the inner and the outer circumference `(a lt b)`, then find the ratio of work done by the person in the two cases shown in the figuer is `W_(1)//W_(2)`. . |
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Answer» Correct Answer - `a^(2)//b^(2)` case `- 1` `F xx a = I alpha rArr alpha = (Fa)/(I)` As `alpha` is constant `omega = alpha t, omega = ((Fa)/(I)) alpha` `W_(1) = Delta KE rArr WD_(1) =(1)/(2) I omega^(2) rArr WD_(1) = (1)/(2) (I) (alpha^(2) t^(2))` `WD_(1) =(1)/(2)I((Fa)/(I))^(2) t^(2)`.....(1) similarly in case II `WD_(2) = (1)/(2) I ((Fb)/(I))^(2) t^(2)` ....(2) from (1) & (2) `(WD_(1))/(WD_(2)) = (a^(2))/(b^(2))`. |
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