Experimental Skills — Instruments & Mechanics Experiments (Medium)

Quick Recap — Measuring Instruments & Mechanics Experiments

• Vernier callipers: least count $=$ 1 MSD $-$ 1 VSD; reading $=$ MSR $+$ (VSD coinciding) $\times$ LC. Screw gauge: LC $=\dfrac{\text{pitch}}{\text{no. of circular divisions}}$; reading $=$ MSR $+$ (CSD) $\times$ LC, corrected for zero error.
• Zero error: positive zero error is subtracted, negative zero error is added.
• Simple pendulum: $g=\dfrac{4\pi^2 L}{T^2}$; time many oscillations to reduce the timing error ($\%g=\%L+2\%T$).
• Young's modulus (Searle's): $Y=\dfrac{MgL}{\pi r^2 \ell}$; sonometer $f=\dfrac{1}{2L}\sqrt{\dfrac{T}{\mu}}$; terminal velocity $v_t=\dfrac{2r^2(\rho-\sigma)g}{9\eta}$.

Worked mini-example. A screw gauge of pitch 1 mm and 100 circular divisions has LC $=\dfrac{1}{100}=0.01$ mm.