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Question

A block of mass 2kg hangs from the rim of a wheel of radius 0.5m.  On releasing from rest the block falls through 5m height in 2s.The moment of inertia of the wheel will be


  1. 1 kg - m2

  2. 3.2 kg - m2

  3. 2.5 kg - m2

  4. 1.5 kg - m2


Solution

The correct option is D

1.5 kg - m2


We have mg - T = ma    ....(1)

Where,

s=ut+12at2

5=0+12×a×4  

a=52ms2    .....(2)

(2) in (1) gives,

20 - T = 5 T = 15N

For the wheel,

TR = I0α

Where a = Rα

Therefore,

T = I0αR2I0=TR2a

I0=15×(0.5)252

=1.5 kg m2

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