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° . 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

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° . 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 (A) (M L2/6) (B) (√2 M L2/24) (C) (M L2/24) (D) (M L2/12)

Tardigrade Admin · Accepted Answer

I=2× ((M/2))((L/2))2× (1/3)=(M L2/12)

Q. A thin rod of length $L$ and mass $M$ is bent at its midpoint into two halves so that the angle between them is $9 0^{\circ} .$ 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

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

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

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

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

$I = 2 \times (\frac{M}{2}) (\frac{L}{2})^{2} \times \frac{1}{3} = \frac{M L ^{2}}{12}$

Q. 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∘. 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

6ML2​

242​ML2​

24ML2​

12ML2​