As shown in the figure, a bob of mass m is tied to a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m . When released from rest the bob starts falling vertically. When it has covered a distance o

Question

As shown in the figure, a bob of mass m is tied to a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m . When released from rest the bob starts falling vertically. When it has covered a distance of h , the angular speed of the wheel will be:

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Correct answer: A. 1 r 4 gh 3

Using work-energy theorem mgh = 1 2 mv 2 + 1 2 Iω 2 mgh = 1 2 mω 2 r 2 + 1 2 mr 2 2 ω 2 ( since I = mr 2 2 and v = rω ) mgh = 3 4 mω 2 r 2 Hence, ω = 4 gh 3 r 2 = 1 r 4 gh 3

As shown in the figure, a bob of mass m is tied to a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m . When released from rest the bob starts falling vertically. When it has covered a distance of h , the angular speed of the wheel will be:

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