Question

Two uniform rod of equal length but different masses are rigidly joined to form L shaped body which is then pivoted as shown. If in equilibrium the body is in the shown configuration ratio M/m will be……. 

(A) 2 

(B) 3 

(C) 2 

(D) √3

Answer 1

Correct option: (D) √3

Explanation: 

from figure, net torque about 0 should be zero hence,

mg ∙ r₁ = Mgr₂ 

(M/m) = (r₁ / r₂)               (1)

since 60 = (r₁ / l) & sin30 = (r₂ / l)

where l is length of each rod hence r₁ = l sin60 = [(l ∙ √3) / 2] & 

r₂ = l sin30 = (l/2) from (1),

(M/m) = [{(√3/2)l} / (l/2)] = √3