The deflection profile $y(x)$ of a cantilever beam due to application of a point force $F$ (in Newton), as a function of distance $x$ from its base, is given by $y(x)=0.001Fx^2[1-\frac{x}{3}]m.$ The angular deformation $\theta$ at the end of the cantilever is measured by reflecting a laser beam off a mirror $\text{M}$ as shown in the figure.
If linear variable differential transformers $\text{(LVDTs)}$ are mounted at $\text x=\frac{1}{2}\text m$ and $\text x=\frac{1}{4}\text m$ on the cantilever to measure the effect of time varying forces, the ratio of their output is
- $\frac{12}{7}$
- $\frac{40}{11}$
- $\frac{176}{23}$
- $\frac{112}{15}$