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Question

Find the moment of inertia of a uniform rod of mass M and length L, about OA {PQ makes an angle of 30 with OA as shown in figure}.


A

ML24

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B

ML212

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C

ML23

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D

ML28

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Solution

The correct option is B

ML212


We can use the very basic formula i.e. I = mr2 in order to find the MI of rod.

Let's assume a small element dx , x units away from point P

Now dm = MLdx

Perpendicular distance of dx from OA

X0 = x sin 30 = x2

Also, dI = dm.x20

= x24MLdx

On integrating,

I = LO M4L x2 dx

= M4L × L33 = ML212


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