Four spheres of diameter 2a and mass M are placed with their centres on the four corners of a square of side b. Then the moment of inertia of the system about an axis along one of the sides of the square is

Four spheres of diameter 2a and mass M are placed with their centres o

1.	Four spheres of diameter 2a and mass M are placed with their centres on the four corners of a square of side b. Then the moment of inertia of the system about an axis along one of the sides of the square is
Answer» `(4)/(5) Ma^(2) + 2 Mb^(2)` `(8)/(5) Ma^(2) + 2 Mb^(2)` `(8)/(5) Ma^2 + Mb^2` `(4)/(5) Ma^(2) + 4 Mb^(2)` SOLUTION : ABCD is a SQUARE of side b . FOUR spheres , each of mass M and radius a are PLACED at the four corners of the square as shown in the figure . We calculate moment of inertia of the system about AD . Moment of inertia of each of the spheres A and D about AD = `(2)/(5) Ma^(2)` Moment of inertia of each of the spheres B and C about AD = `((2)/(5) Ma^(2) + Mb^(2))` , using THEOREM of parallel axes. `therefore` Total moment of inertia of the system about AD ` = 2[(2)/(5) Ma^(2) + ((2)/(5) Ma^(2) + Mb^(2))] = (8)/(5) Ma^(2) + 2 Mb^(2)`