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the moment of inertia of a solid cylinder about its own axis is the same as its moment of inertia about an axis passing through its centre of gravity and perpendicular to its length.the relation between its length L and radius R is---. Explain???

the moment of inertia of a solid cylinder about its own axis is the same as its moment of inertia about an axis passing through its centre of gravity and perpendicular to its length.the relation between its length L and radius R is---. Explain???

Grade:11

2 Answers

Shrimay kher
19 Points
7 years ago
L2 = 3R2
as MI of a solid cylinder about its own axis is ½ MR2
and MI about an axis passing through its centre of gravity and perpendicular to its length is
M(L2/12 + R2/4)
 ½ MR2 = M(L2/12 + R2/4)
R2/2 = L2/12 + R2/4
R2/2 – R2/4 = L2/12
L2 = 3R2
L1/2 = 31/2 R
Yash Chourasiya
askIITians Faculty 256 Points
3 years ago
Dear Student

Moment of Inertia about axis of cylinder = 1/​2(mR2)........(1)
Moment of Inertia about axis passing through center of gravity and perpendicular to its length = m((L2/12​) +(R2/4)​).......(2)

From equation (1) and (2),
we get
​√3R=L

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya

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