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A wheel of radius 0.4m can rotated freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4kg is hung, An angular acceleration of $8 rad - s^{- 2}$ is produced in it due to the torque. Then moment of inertia of the wheel is $(g = 10 {ms}^{- 2})$

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$8 kg - m^{2}$

$2 kg - m^{2}$

$1 kg - m^{2}$

$1.36 kg - m^{2}$

answer is C.

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Detailed Solution

$τ = I α = r F$

$M g - T = m a; a = r α$

$T = 4 [10 - (0.4 \times 8)]$

$T r = I α$

using the value of T.

We get I= $1.36 kg - m^{2}$

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