A circular disc of radius ' R ' and thickness R 8 has moment of inertia 'I' about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere then moment of inertia of sphere about an axis passing through diameter is

Step-by-step solution

M.I. of disc, I= 1 2 M R_d^2 M.I. of sphere, I _ sphere = 2 5 MR _ s ^2 volume of disc = volume of sphere (given) array ll & R _ d ^2 ( R _ d 8 )= 4 3 R _ s ^3 & R _ d ^3= 32 R _ s ^3 3 & R _ s = ( 3 32 )^ 1 / 3 R _ d ...(i) array Substitute equation (iii) in equation (ii) aligned I _ sphere & = 2 5 M ( 3 32 )^ 2 / 3 R _ d ^2 & 1 5 ( 2 5 MR _ d ^2 )= 1 5 aligned [From (i)]