Q. Students I, II and III perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the table Least count for length $= 0.1\ cm$ Least count for time $= 0.1\ s$ [table] Stud ent | Length of the pend ulum $(cm)$ | Number of oscilla tion $(n)$ | Total time for $(n)$ oscilla tions $\ (s)$ | Time period $\ (s)$ I | 64.0 | 8 | 128.0 | 16.0 I | 64.0 | 4 | 64.0 | 16.0 III | 20.0 | 4 | 36.0 | 9.0 [/table] If $E_{I},\ E_{II}$ and $E_{III}$ are the percentage errors in $g,\ i.e.,\ \left( \frac{\mathrm{\Delta}g}{g} \times 100 \right)$ for students I, II and III, respectively
A) $E_{I} = 0$
B) $E_{I}$ is minimum
C) $E_{I} = E_{II}$
D) $E_{II}$ is maximum
Explanation
$\%$ error in $g = \frac{\mathrm{\Delta}g}{g} \times 100 = \left( \frac{\mathrm{\Delta}l}{l} \right) \times 100 + 2\left( \frac{\mathrm{\Delta}T}{T} \right) \times 100$ $E_{I} = \frac{0.1}{64} \times 100 + 2\left( \frac{0.1}{128} \right) \times 100 = 0.3125\%$ $E_{II} = \frac{0.1}{64} \times 100 + 2\left( \frac{0.1}{64} \right) \times 100 = 0.4687\%$ $E_{III} = \frac{0.1}{20} \times 100 + 2\left( \frac{0.1}{36} \right) \times 100 = 1.055\%$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.