Question

A rough casting of a rotor, with a mass of 200 kg, is mounted on centres 110 cm apart for machining. The rotor is statically balanced by attaching two masses, one each in the planes A (9 kg) and B (12 kg), which are on opposite sides of the plane containing the mass centre of the rotor, at a distance of 50 cm and 35 cm respectively from it. The angle between the CG of the plane A and that of the plane B is 90${}^{\circ }$. The distance of each mass from the axis of rotation is 37 cm (for the plane A) and 44 cm (for the plane B).

The distance of the CG of the rotor from the axis of rotation, and its angular position with respect to the mass in the plane A respectively are

• A. $3.12\text{cm,}{237.76}^{\circ }$
• B. $3.12\text{cm,}{57.76}^{\circ }$
• C. $4.12\text{cm,}{67}^{\circ }$
• D. $4.12\text{cm,}{247}^{\circ }$

Answer 1

The correct option is A $3.12\text{cm,}{237.76}^{\circ }$


$m_A=9\text{kg,}{m}_B=12\text{kg,}$

$r_A=37\text{cm,}{m}_A=44\text{cm}$

$N=100\text{rpm}$

$\omega =\frac{2\pi N}{60}=10.47\text{rad/sec}$

As the rotor is statically balanced
$200\times r=\sqrt{(9\times 37{)}^{+}(12\times 44{)}^2}$

$\Rightarrow r=3.12\text{cm}$

$\tan \theta =\frac{m_B{r}_B}{m_A{r}_A}=\frac{12\times 44}{9\times 37}$

$\Rightarrow \theta ={57.76}^{\circ }$