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Q.

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

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a

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

b

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

c

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

d

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

answer is B.

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Detailed Solution

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Moment of inertia of the ring is ${MR}^{2}$ and that of each spoke is $\frac{{mR}^{2}}{3}$ .

Total moment of inertia ${MR}^{2} + \frac{{mR}^{2}}{3} \times 3 = (M + m) R^{2}$

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