A circular disc of radius R and thickness R 6 has moment inertia I about an axis passing through its centre perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter is

Step-by-step solution

According to problem disc is melted and recasted into a solid sphere so their volume array c will be same. V_ Disc =V_ Sphere R_ Disc ² t= 4 3 R_ Sphere ³ R_ Disc ² ( R_ Disc 6 )= 4 3 R_ Sphere ³ [t= R_ Disc 6 , given ] R_ Disc ³=8 R_ Sphere ³ R_ Sphere = R_ Disc 2 array Moment of inertia of disc array l I_ Disc = 1 2 M R_ Disc ²=I (given) M (R_ Disc )²=2 I array Moment of inertia of sphere array l I_ Sphere = 1 2 M R_ Sphere ² = 2 5 M ( R_ Disc 2 )²= M 10 (R_ Disc )²= 2 I 10 = I 5 array