Two masses 1.2kg and 1.8kg are connected to the ends of a rod of length 2m. Find the moment of inertia about the axes, 1)going through the mid point of the rod. 2)going through the centre of mass of two masses.

Answers: 1) 3 kg m²

                2) 2.88 kg m²

Explanation: Question 1

                      I = m(r)²+ M(r)²

                      I = 1.2 kg × (1 m )² +1.8 kg ×(1 m )²

                    ∴  I =   3 kg m²

                      Question 2

ACCORDING TO THE DIAGRAM DRAWN FOR QUESTION 2

we have to decide where the center of gravity (G) lies and obviously it should lie somewhere near to the greater mass. (which is 1.8 kg). Since we don't know the distance from center of gravity(G) to the mass (1.8 kg) we'll take it as 'x' and solve!!

moments around 'G'

F₁ d ₁ = F₂ d ₂

12 (2-X) = 18 (X)

24 -12 X =18 X

∴  X = 0.8 m

∴ ( 2 - x ) = 1.2 m

∴ Moment of inertia (I) going through the center of mass of two masses,

⇒ I = m (r)² +M (r)²

⇒ I = 1.2 × (1.2)² + 1.8 × (0.8)²

⇒ I = 1.2 × 1.44 + 1.8 × 0.64

⇒ I = 1.728 + 1.152

⇒ ∴ I = 2.88 kg m²

∴ THE QUESTION IS SOLVED !!!

a is the best answer your welcome