A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of 10 grams, attached to four points on the 100 mm radius circle shown in the figure.

The rotor is driven by a motor at uniform angular speed of 10 rad/s. If one of the masses gets detached then the magnitude of the resultant unbalance force on the rotor is ______ N. (round off to 2 decimal places).

The correct answer is 0.10

1. Understanding the Initial Balanced State:
As shown in the provided figure, there are four identical point masses labeled as A, B, C, and D attached to the rotor at a radius of r = 100 mm. These masses are positioned symmetrically at 90-degree intervals along the horizontal and vertical axes. Specifically, mass A balances mass C, and mass B balances mass D. Since the centrifugal forces exerted by these opposing pairs are equal in magnitude and opposite in direction, the net unbalance force is initially zero, and the system is balanced.

2. Effect of Detaching One Mass:
When one of the masses (for example, mass A) is detached, the remaining three masses (B, C, and D) are no longer symmetrically balanced. Mass B and mass D are still opposite to each other and their centrifugal forces cancel out. However, mass C no longer has mass A to balance its centrifugal force. Therefore, the magnitude of the resulting net unbalance is equivalent to a single point mass of 10 grams located at a radius of 100 mm.

3. Calculating the Unbalance Force:
The magnitude of the unbalance centrifugal force is given by the formula:

Funbalance=m·r·ω2

Where the parameters are given as:
Mass,
m=10 g=10×10-3 kg=0.01 kg
Radius,
r=100 mm=0.1 m
Angular speed,
ω=10 rad/s

Substituting the values into the formula:

Funbalance=0.01×0.1×102

Funbalance=0.01×0.1×100=0.10 N

Thus, the magnitude of the resultant unbalance force on the rotor is 0.10 N.