Question

Four identical particles of mass m are mounted at equal intervals on a thin rod of length l and mass m, with one mass at each end of the rod.

Answer 1

Moment of inertia at distance L / 2 from center

I1 = M (L / 2)^2 = M L^2 / 4

I2 = M (L / 6)^2 = M L^2 / 36 at a distance of L / 6

I (1/2 rod) = I1 + I2 = M L^2 (1/4 + 1/36) = M L^2 (9 + 1)/ 36 = 5/ 18 M L^2

I for entire rod = 2 I (1/2 rod) = 5 / 9 M L^2