Question

Three particles are arranged as shown in the figure. 

1. Find the position of their centre of mass. 

2. Find M.I. about an axis perpendicular to plans and passing through CM. 

3. Find M.I. about an axis perpendicular to plane and passing through A and hence show that parallel axes theorem holds good. 

4. Find M.I. about AQ.

Answer 1

1. Co-ordinates of B (0, 0) Co-ordinates of C (a, 0) Co-ordinates of A 

Hence CM is the centroid of the triangle as shown

The Co-ordinates of CM is 

The distance of CM from A, B, or C is same and d is

∴ M.l. about an axis ⊥ to triangle and passing and through CM = ma²

3. M.I.about an axis perpendicular to plane and passing through A is,

IA = Σ m_i x_i²

= m_A(0) + mB(a²) + m_C(a°)

= I_CM + (3m) d²

= ma² + ma² = 2ma²

LHS = RHS

Hence parallel axes theorem is verified