Question

13. Two masses of 3 kg and 5 kg are placed at 30 cm and 70 cm marks respectively on a light wooden metre scale. What will the moment of inertia of the system about an axis through (i) 0 cm mark and (ii) 100 cm mark, and perpendicular to the metre scale ?
[Ans. (i) 2.72 kg m² (ii) 1.92 kg m2?]​

Answer 1

The moment of inertia across the zero mark is 4.4 kg-m and through the 100 mark is 3.6 Kg-m.

Explanation:

Moment of inertia = Σmiri

Moment of inertia of the system about the axis passing through the zero mark on the scale.

m1 = 3 Kg

m2 = 5 Kg

r1  = 30 cm = 0.3 m

r2 = 70 cm = 0.7 m

I = m1r1 + m2r2

I = 3 x 0.3 + 5 x 0.7 = 4.4 kg-m

Moment of inertia of the system about the axis passing through the 100 mark on the scale.

m1 = 3 kg

m2 = 5 kg

r1 = ( 100 - 30) = 70 cm = 0.7 m

r2 = ( 100 - 70 ) = 30 cm = 0.3 m

I' = m1r1 x m2r2 = 3 x 0.7 + 5 x 0.3

I' = 3.6 Kg-m

Hence the moment of inertia across the zero mark is 4.4 kg-m and through the 100 mark is 3.6 Kg-m.

Also learn more

The moment of inertia of a uniform rod of mass 0.50 kg and length 1 m is 0.10 kg-m² about a line perpendicular to the rod. Find the distance of this line from the middle point of the rod?

https://brainly.in/question/4573586

Answer 2

(i) 2.72 kg m² (ii) 1.92 kg m2

Explanation:

(i) at axis (0 cm mark)

 m₁r₁² + m₂r₂² = 3 (0.3)² + 5 (0.7)²

   = 0.27 + 2.45

   = 2.72 kgm²

(ii) at axis (100 cm mark)

   m₁r₁² + m₂r₂² = 5 (0.3)² + 3 (0.7)²

   = 0.45 + 1.47

   = 2.72 kgm²

Thus, the correct answer is = (i) 2.72 kg m² (ii) 1.92 kg m²

Learn more,

moment of inertia : brainly.in/question/4573586