Practicing Success
If $T=2 \pi \sqrt{\frac{l}{g}}$, then relative errors in T and l are in the |
1/2 2 1/2 π none of these |
1/2 |
We have, $T=2 \pi \sqrt{\frac{l}{g}}$ $\Rightarrow \log T=\log 2 \pi+\frac{1}{2} \log l-\frac{1}{2} \log g$ $\Rightarrow \frac{1}{T} d T=0+\frac{1}{2 l} d l-0 $ $\Rightarrow \frac{d T}{T}=\frac{1}{2} \frac{d l}{l}$ $\Rightarrow \frac{\Delta T}{T}=\frac{1}{2} \frac{\Delta l}{l}$ $[∵ d T \cong \Delta T$ and $d l \cong \Delta l]$ $\Rightarrow \frac{\frac{\Delta T}{T}}{\frac{\Delta l}{l}}=\frac{1}{2}$ |