Home
Class 12
PHYSICS
A thin rod of length 4l, mass 4 m is ben...


A thin rod of length 4l, mass 4 m is bent at the point as shown in the figure. What is the moment of inertia of the rod about the axis passing through O and perpendicular to the plane of the paper?

A

`(m l^(2))/(3)`

B

`(10m l^(2))/(3)`

C

`(m l^(2))/(12)`

D

`(m l^(2))/(24)`

Text Solution

Verified by Experts

The correct Answer is:
B
A thin rod ……………..
The given structure can be broken into 4 parts

For `AB : I = I_(CM)+mxxd^(2)=(ml^(2))/(12)+(5m)/(4)l^(2)`
`, I_(AB)=(4)/(3)ml^(2)`
For `BO : I = (m l^(2))/(3)`
`:.` For composite frame : (by symmetry)
`I = 2[I_(AB)+I_(OB)]= 2[(4m l^(2))/(3)+(m l^(2))/(3)] = (10)/(3)m l^(2).`]
Promotional Banner

Similar Questions

Explore conceptually related problems

A thin rod of length L of mass M is bent at the middle point O at an angle of 60^@ . The moment of inertia of the rod about an axis passing through O and perpendicular to the plane of the rod will be

A uniform rod of mass m is bent into the form of a semicircle of radius R. The moment of inertia of the rod about an axis passing through A and perpendicular to the plane of the paper is

Two identical rods each of mass M and length L are kept according to figure. Find the moment of inertia of rods about an axis passing through O and perpendicular to the plane of rods.

Two rods each having length l and mass m joined together at point B as shown in figure.Then findout moment of inertia about axis passing thorugh A and perpendicular to the plane of page as shown in figure.

A particle mass m is attched to a thin uniform rod of length a at a distance of (a)/(4) from the mid-point C as shown in the figure. The mass of the rod is 4m The moment of inertia of the combined system about an axis passing through O and perpendicular to the rod is

A thin wire of length l and mass m is bent in the form of a semicircle as shown in the figure. Its moment of inertia about an axis joining its free ends will be