Manipal Entrance Test 2013 Physics Paper

Let the radii of the thin spherical and the solid sphere are R1 and R2 respectively
Then the moment of inertia of the spherical shell about their diameter
I=

2

3

MR12 ....(i)
and the moment of inertia of the solid sphere is given by
I=

2

3

MR22 ....(ii)
Given that the masses and moment of inertia for both the bodies are equal, then from Eqs. (i)and (ii)

2

3

MR12=

2

3

MR22
⇒

R12

R22

=

3

5

⇒

R1

R2

=√

3

5

⇒ R1:R2=√3:√5