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A wheel comprises of a ring of radius R and mass M and three spokes of mass m each. The moment of inertia of the wheel about its axis is

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$(M + \frac{m}{4}) R^{2}$

$(M + m) R^{2}$

$(M + 3 m) R^{2}$

$(\frac{M + m}{2}) R^{2}$

answer is B.

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Detailed Solution

$I = I_{ring} + 3 I_{spoke} = M R^{2} + 3 (\frac{m R^{2}}{3}) = (M + m) R^{2}$

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