Question

3 small balls A,B,C of masses 40 gm,10gm&25gm are connected by straight right & light rods AB,BC,CA of length 5cm,2cm,4cm respectively.what is the moment of inertia of the system about an axis passing through A perpendicular to the plane of system?

Answer 1

ABC is a triangle as shown in figure.

[ as you know, properties of triangle are ;

• sum of two sides of triangle is always great than 3rd side. i.e, 5 + 2 > 4, 2 + 4 > 5, 5 + 4 > 2
• difference of two sides of triangle is always less than 3rd side. i.e., 5 - 2 < 4, 4 - 2< 5, 5 - 4 < 2

so, this way we can say points A, B and C form triangle. ]

now, moment of inertia about XX' (see figure ) = $m_Br_B^2+m_Cr_C^2$

= 10g × (5cm)² + 25g × (4cm)²

= 10 × 25 + 25 × 16

= 250 + 400

= 650 gcm²

= 650 × 10^-3 kg × (10^-2m)²

= 650 × 10^-7 Kg m²