SATHEE: Rotational Motion Question 66

Rotational Motion Question 66

Question: A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is $90^{o}$ . The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is

[AIPMPT (S) 2008]

Options:

A) $\frac{M L^{2}}{24}$

B) $\frac{M L^{2}}{12}$

C) $\frac{M L^{2}}{6}$

D) $\frac{\sqrt{2} M L^{2}}{24}$

Show Answer

Answer:

Correct Answer: B

Solution:

Since rod is bent at the middle, so each part of it will have same length $(\frac{L}{2})$ and mass $(\frac{M}{2})$ as shown.

Moment of inertia of each part through its one end $= \frac{1}{3} (\frac{M}{2}) {(\frac{L}{2})}^{2}$

Hence, net moment of inertia through its middle point O is

$I = \frac{1}{3} (\frac{M}{2}) {(\frac{L}{2})}^{2} + \frac{1}{3} (\frac{M}{2}) {(\frac{L}{2})}^{2}$

$= \frac{1}{3} [\frac{M L^{2}}{8} + \frac{M L^{2}}{8}] = \frac{M L^{2}}{12}$

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Rotational Motion Question 66

Question: A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90o . The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is

Options:

Answer:

Solution:

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Question: A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is $90^{o}$ . The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is