Question

The string of a simple pendulum is found to have a mass which is one-tenth that of the pendulum bob. The systematic error in the measurement of g due to neglecting the string mass is approximately

• A. 0%
• B. 5%
• C. 10%
• D. 20%

Answer 1

The correct option is B 5%

$T=2\pi \sqrt{\frac{l}{g}}$

Here, $l$=distance of center of mass from point of suspension.

$m_s$=string mass and $m_b=$ bob mass

In figure, $x$=distance of final center of mass from lower end.

Now, $x=\frac{m_s}{m_b}\frac{l}{2}$

$⟹x=\frac{1}{10}\frac{l}{2}=\frac{l}{20}=l-l^{{}^{\prime }}$

$⟹\Delta l=\frac{l}{20}$

$\frac{\Delta l}{l}=\frac{1}{20}$

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

$⟹\frac{\Delta g}{g}=\frac{\Delta l}{l}=\frac{1}{20}=5\%$

Hence, answer is option-(B).