Four spherical particles, each of mass m and radius r are kept at the four corners of a square of side a Moment of inertia of the system along a side of the square is

Options

A. `4m[2/5r^2+a^2]`
B. `4m[2/7r^2+a^2]`
C. `2m[4/5r^2+a^2]`
D. `2m[4/7r^2+a^2]`

Answer

C

Explanation

Moment of inertia of the two spheres lying on the axis of rotation it self is `2 xx2/5 mr^2` Moment of inertia of the two spheres lying on.other two corners (using parallel axes theorem) is = 2 ( `2/5 "mr"^2+ ma^2)`

Total moment of inertia `=2[2/5mr^2+2/5 mr^2 +ma^2]=8/5 mr^2+2ma^2=2m[4/5r^2+a^2]`