Three identical particles are fixed to the corners of an isosceles right angled triangle by means of mass less connecting rods….

Q: Three identical particles are fixed to the corners of an isosceles right angled triangle by means of mass less connecting rods. Each of the two equal sides has a length d . The moment of inertia of this rigid object when the axis of rotation coincides with the hypotenuse of the triangle is: (mass of each particle = m)

(a) $\displaystyle \frac{1}{2} m d^2 $

(b) $\displaystyle \frac{1}{4} m d^2 $

(c) $\displaystyle m d^2 $

(d) $\displaystyle \frac{3}{4} m d^2 $

Ans: (a)

Moment Of Inertia $\displaystyle I = m_1 r_1^2 + m_2 r_2^2 + m_3 r_3^2 $

Moment of Inertia due to two masses is zero because two masses lie on the axis , r1 = 0 & r2 = 0

$\displaystyle I = m \times 0 + m \times 0 + m \times (\frac{d}{\sqrt{2}})^2 $

$\displaystyle I = \frac{1}{2} m d^2 $