Question

Figure shows the kinetic energy $K$ of a simple pendulum versus its angle $\theta$ from the vertical. The pendulum bob has mass $0.2\, kg$. The length of the pendulum in meter $\left(g=10\, m / s ^{2}\right)$ is___

Answer 1

Given that from graph
$\frac{1}{2} m V_{m}^{2}=15 \times 10^{-3}$
$V_{m}=\sqrt{0.150} \,m / s$
$A \omega=\sqrt{0.150} \,m / s$
$L \theta_{m} \cdot \sqrt{\frac{g}{L}}=\sqrt{0.150} \,m / s$
$\Rightarrow \sqrt{g L}=\frac{\sqrt{0.150}}{100 \times 10^{-3}} $
$\Rightarrow L=\frac{0.150}{0.1}=1.5\, m $