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Q.

The moment of inertia of a rod about an axis through its centre and perpendicular to its length 1/12 ML² (where, M is the mass and L the length of the rod) The rod is bent in the middle so that the two halves make an angle of 60^o. The moment of inertia of the bent rod about an axis passing through the bend point and perpendicular to its plane is __

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a

$\frac{{ML}^{2}}{8 \sqrt{2}}$

b

1/48 ML²

c

1/12 ML²

d

1/24 ML²

answer is B.

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Detailed Solution

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MI about a perpendicular axis of the bent rod will be

$I = \frac{(\frac{m}{2}) {(\frac{l}{2})}^{2}}{3} + \frac{(\frac{m}{2}) {(\frac{l}{2})}^{2}}{3}$

$I = \frac{(\frac{m}{2}) {(\frac{l}{2})}^{2}}{3} x 2$

$I = \frac{m l^{2}}{12}$

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The moment of inertia of a rod about an axis through its centre and perpendicular to its length 1/12 ML2 (where, M is the mass and L the length of the rod) The rod is bent in the middle so that the two halves make an angle of 60o. The moment of inertia of the bent rod about an axis passing through the bend point and perpendicular to its plane is __