Question

A rod of length L and of negligible mass is pivoted at a point that is off-center with lengths shown in the figure below. The figures show two cases in which masses are suspended from the ends of the rod. In each case the unknown mass m is balanced by a known mass, M₁ or M₂, so that the rod remains horizontal. What is the value of m in terms of the known masses?

(A) M₁ + M₂ 

(B) ½(M₁ + M₂) 

(C) M₁ M₂ 

(D) ½M₁M₂  

(E) √(M₁ M₂)

Answer 1

Correct option  (E) √(M₁ M₂)

Applying rotational equilibrium to each diagram gives