InterviewSolution
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InterviewSolution
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A mass `m` is attached to a pulley through a cord as shown in figure. The pulley is a solid disk with radius `R`. The cord does not slip on the disk. The mass is released from rest at a height `h` from the ground and at the instant the mass reaches the ground, the disk is rotating with angular velocity `omega`. Find the mass of the disk. . |
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Answer» Correct Answer - (i) `M = 2m((2gh)/(R^(2) omega^(2))-1)` By work Energy Theorem `WD_(g) = Delta KE` `mgh = (1)/(2) mv^(2) + (1)/(2) omega^(2)` `mgh = (1)/(2) m(R omega)^(2) + (1)/(2) xx((1)/(2) MR^(2)) omega^(2)` (M = mass of disc) `mgh = (1)/(2) mR^(2) omega^(2) + (1)/(4) MR^(2) omega^(2)` `mgh -(1)/(2) MR^(2) omega^(2) = (1)/(4) MR^(2) omega^(2)` `M = (4(mgh -(1)/(2) mR^(2) omega^(2)))/(R^(2) omega^(2))` `M = 2m((2gh)/(R^(2)omega^(2)) -1)`. |
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