Question

In a flyball-type angular speed magnitude measuring device, the centrifugal force, given ${10}^{-6}{\omega }^2$, where $\omega$ is the angular speed in rad/s, is transmitted to a spring with the non-linear characteristic $F=16{\pi }^2{x}^2$, where F is the applied force and $x$ is the spring compression in meters. The sensitivity of the device in mm/s is

• A. $\frac{1}{\pi }$
• B. $\frac{1}{2\pi }$
• C. $\frac{1}{3\pi }$
• D. $\frac{1}{4\pi }$

Answer 1

The correct option is D $\frac{1}{4\pi }$

Balancing forces we get,

${10}^{-6}{\omega }^2=16{\pi }^2{x}^2$

$\therefore \frac{x^2}{{\omega }^2}=\frac{{10}^{-6}}{16{\pi }^2}$

$\therefore sensitivity\left(\frac{x}{\omega }\right)=\frac{{10}^{-3}}{4\pi }m/sec.$

$=\frac{1}{4\pi }mm/sec$