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

Step-by-step solution

M.I. of disc, I= 1 2 MR _ d ^2 ... (i) M.I. of sphere, I_ sphere = 2 5 MR _ s ^2 ... (ii) volume of disc = volume of sphere array ll & R _ d ^2 ( R _ d 6 )= 4 3 R _ s ^3 & R _ d ^3=8 R _ s ^3 & R _ S = R _ d 2 ... (iii) array Substitute equation (iii) in equation (ii) aligned I _ sphere & = 2 5 M ( R _ d 2 )^2= 2 5 1 4 MR _ d ^2 & = 1 5 ( 1 2 MR _ d ^2 )= I 5 ....[from (i)] aligned