Two masses are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal mass m₁ is attached to the opposite sides of the shaft in the vertical plane as shown in the figure. Consider m = 1 Kg, e = 50 mm, e₁ = 20 mm, b = 0.3 m, a = 2 m and a₁ = 2.5 m. For the system to be dynamically balanced m₁ should be

Question

Question

This question was previously asked in

ISRO MCF Technical Assistant Mechanical 23 June 2019 Official Paper

Answer 1

Concept:

For dynamic equilibrium,

∑ F = 0 & ∑ M = 0 about any is valid.

Calculation:

Given:

m = 1 kg, e = 50 mm, e1 = 20 mm, b = 0.3 m, a = 2 m, a1 = 2.5 m.

By symmetry we have,

meω2 + m1e1ω2 = m1e1ω2 + meω2

Clearly ∑ F = 0

Now for moment,

We will balance all the moment due to forces except reaction, about point O

meω2 × (b) + m1e1ω2 × a1 – meω2 × (a + b) = 0

m1e1ω2 × a1 – meω2 × a = 0

m₁ = 2 kg.

Download Solution PDF