Topic: Theory of Machines
In the statement, an eccentric mass rotating at 3000 rpm will create X times more unbalanced force than 50% of the same mass rotating at 300 rpm, X will be
- A. 10
- B. 50
- C. 100
- D. 200
Answer: D. 200
Explanation: Unbalanced centrifugal force is given by $F = mr\omega^2$.
Force case 1 ($F_1$): mass $m_1 = m$, speed $N_1 = 3000~rpm$.
Force case 2 ($F_2$): mass $m_2 = 0.5m$, speed $N_2 = 300~rpm$.
$X = \frac{F_1}{F_2} = \frac{m_1 N_1^2}{m_2 N_2^2} = \frac{m \times 3000^2}{0.5m \times 300^2} = 2 \times \left(\frac{3000}{300}\right)^2 = 2 \times 10^2 = 200$.