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 is equal to $\left(g=10 \,m / s ^{2}\right)$ :

• A. 2.0 m
• B. 1.8 m
• C. 1.5 m
• D. 1.2 m

Answer 1

Answer: (C)

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 $