Question

Moment of inertia of a solid cylinder of length l and diameter d about an axis passing through its centre of gravity and perpendicular to its geometric axis is.

Answer 1

Given:

The moment of inertia I

The diameter is d

The radius be r

The length be L

To find:

The relation between length L  and r

Solution:

The moment of inertia f the cylindrical

I=mr²/2

The moment of inertia of length L and radius r

I=m(L²/12 + R²/4)

I=m(L²+3r²)/12

Now equating the above values

mr²/2=m(L²+r²)/12

6r²=L²+3r²

3r²=L²

√3r=L

The relation between the radius and length is √3r=L