Physics - Rotation Question with Solution | TestHub

As shown in the figures, a uniform rod $O{O}^{\prime }$ of length $\ell$ is hinged at the point $O$ and held in place vertically between two walls using two massless springs of same spring constant. The springs are connected at a point P and at the top-end $\left(O^{\prime }\right)$ of the rod, as shown in Fig. 1 and the rod is made to oscillate by a small angular displacement. The frequency of oscillation of the rod is $f_1$. On the other hand, if both the springs are connected at the point P of the rod, as shown in Fig. 2 and the rod is made to oscillate by a small angular displacement, then the frequency of oscillation is $f_2$. Ignoring gravity and assuming motion only in the plane of the diagram, the value of $\frac{{\mathrm{f}}_1}{{\mathrm{f}}_2}$ is :-