Figure shows a counterweight of mass m suspended by a cord wound around a spool of radius r, forming part of a turntable supporting the object. The turntable can rotate without friction. When the counterweight is released from rest, it descends through a distance h, acquiring a speed v. The moment of inertia I of the rotating apparatus is
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a
mr2(2ghv2+1)
b
mr2(ghv2-1)
c
mr2(2ghv2-1)
d
mr2(ghv2+1)
answer is C.
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Detailed Solution
Each point on the cord moves at a linear speed of v = ωr where r is the radius of the spool. The energy conservation equation for the counter weight turn table-Earth system is:(K1+K2+Ug)i+Wother = (K1+K2+Ug)fSpecializing, we have0+0+mgh+0 = 12mv2+12Iω2+0mgh = 12mv2+12Iv2r22mgh -mv2 = Iv2r2 and finally, I = mr2(2ghv2-1)
Figure shows a counterweight of mass m suspended by a cord wound around a spool of radius r, forming part of a turntable supporting the object. The turntable can rotate without friction. When the counterweight is released from rest, it descends through a distance h, acquiring a speed v. The moment of inertia I of the rotating apparatus is