Experimental Skills — Advanced Practice & Error Analysis (Hard)

Quick Recap — Advanced Experiments & Error Analysis (Multi-step)

• Instrument readings: total $=$ MSR $+$ (coinciding division) $\times$ LC, then apply the zero-error correction (subtract positive, add negative).
• $g$ from a pendulum: $g=\dfrac{4\pi^2 L}{T^2}$; $\%g=\%L+2\%T$ (timing dominates).
• Young's modulus: $Y=\dfrac{MgL}{\pi r^2\ell}\Rightarrow\%Y=\%M+\%L+2\%r+\%\ell$.
• Metre bridge / potentiometer: $X=R\dfrac{l}{100-l}$; $r=R\dfrac{l_1-l_2}{l_2}$.

Worked mini-example. Screw gauge (LC 0.01 mm, zero error $-0.02$ mm): MSR 3 mm, 45th division coincides. Reading $=3+45\times0.01=3.45$ mm; correcting the negative zero error: $3.45+0.02=3.47$ mm.