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 !!!
