Question

Students $I,IIandIII$ 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 $=0.1cm$
Least count for time $=0.1s$

Student	Length of the pendulum (cm)	Number of oscillations (n)	Total time for (n) oscillations (s)	Time period (s)
I	64.0	8	128.0	16.0
II	64.0	8	64.0	16.0
III	20.0	4	36.0	9.0

If $E_I,E_{II}$ and $E_{III}$ are the percentage errors in $g$, i.e., $(\frac{\Delta g}{g}\times 100)$ 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

Answer 1

Answer: (B)

$E_I$ is minimum

Time period of a simple pendulum can be given by $T=2\pi \sqrt{\frac{l}{g}}$.

$\Rightarrow g=\frac{4{\pi }^{2}l}{T^2}$

$\Rightarrow \frac{\Delta g}{g}=\frac{\Delta l}{l}+\frac{2\Delta t}{t}$.

So, the $\frac{\Delta g}{g}$ decreases with larger t value.

Hence, dfractional error in the 1st observation is minimum.

Ans: B