1. **Stating the problem:** We have two graphs to plot and analyze: - Graph 1: Log T against Log L - Graph 2: T² against L We need to find the slope and intercept of the first graph, the slope of the second graph, and then deduce the value of gravitational acceleration $g$ from these graphs. 2. **Relevant formulas and rules:** For a simple pendulum, the period $T$ is related to the length $L$ and gravitational acceleration $g$ by: $$T = 2\pi \sqrt{\frac{L}{g}}$$ Taking logarithms on both sides: $$\log T = \log (2\pi) + \frac{1}{2} \log L - \frac{1}{2} \log g$$ This is a linear relation between $\log T$ and $\log L$ with slope $\frac{1}{2}$. Also, squaring the period: $$T^2 = 4\pi^2 \frac{L}{g}$$ This is a linear relation between $T^2$ and $L$ with slope $\frac{4\pi^2}{g}$. 3. **Graph 1: Log T vs Log L** - The slope $m_1$ of the line is theoretically $\frac{1}{2}$. - The intercept on the $\log L$ axis occurs when $\log T = 0$, so: $$0 = \log (2\pi) + \frac{1}{2} \log L - \frac{1}{2} \log g$$ Solving for $\log L$: $$\frac{1}{2} \log L = \frac{1}{2} \log g - \log (2\pi)$$ $$\log L = \log g - 2 \log (2\pi)$$ 4. **Graph 2: $T^2$ vs $L$** - The slope $m_2$ is: $$m_2 = \frac{4\pi^2}{g}$$ 5. **Deducing $g$ from the graphs:** - From Graph 2 slope: $$g = \frac{4\pi^2}{m_2}$$ - From Graph 1 slope and intercept, since slope is $\frac{1}{2}$, the intercept can be used to find $g$ if measured. 6. **Summary:** - Plot $\log T$ vs $\log L$, slope should be $\frac{1}{2}$. - Plot $T^2$ vs $L$, slope $m_2$ gives $g = \frac{4\pi^2}{m_2}$. - Compare $g$ values from both graphs for consistency. This completes the analysis and method to find $g$ from the given graphs.