Question

Two discs of moment of inertia I₁ and I₂ and angular speeds ω₁ and ω₂ are rotating along collinear axes passing through their centre of mass and perpendicular to their plane. If both discs are pressed face to face to rotate combinedly along same axis, then rotational KE of system is

(a) \(\frac{I_1ω _1 +\,I_2ω _2}{2(I_1 + I_2)}\)

(b) \(\frac{(I_1\, + I_2)(ω _1 + ω _2)^2}{2}\)

(c) \(\frac{(I_1ω _1 +\,I_2ω _2)^2}{2(I_1 + I_2)}\)

(d) None of these

Answer 1

Correct option:  (c) \(\frac{(I_1ω _1 +\,I_2ω _2)^2}{2(I_1 + I_2)}\)

According to law of conservation of angular momentum,