Find the moment of inertia of a uniform solid sphere of mass,m and radius,a about an axis through its centre.(adsbygoogle = window.adsbygoogle || []).push({});

I have tried to solve it but I get the different answer, I don't know where I have done mistake. Please! check and correct my solution below:-

Consider a volume element, dv of the sphere; this has mass,mdv/(4/3)∏a^3.

Then

I = ∫(mdv/(4/3)∏a^3)r^2

Where r is the distance of the volume element, dv from the axis, and

I is the moment of inertia

I = m/(4/3)∏a^3∫r^2dv

We know, the volume of the sphere,v is:

v = (4/3)∏r^3

dv = 4∏r^2dr

Thus,

I = 3m/(4/3)∏a^3∫r^2(4∏r^2)dr

= 3m/a^3∫r^4dr under limit [0,a]

= 3m/a^3[r^5/5] under [o,a]

Hence,

I = (3/5)ma^2 --------------WRONG!!!

The correct answer is: I = (2/5)mr^2

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# Uniform Solid Sphere

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