Question

The percentage errors in the measurement of length and time period of a simple pendulum are 1% and 2% respectively. Then the maximum error in the measurement of acceleration due to gravity is

• A. 8%
• B. 3%
• C. 4%
• D. 6%
• E. 5%

Answer 1

Answer: (E)

Time period of simple pendulum is
$T=2\pi \sqrt{\frac{l}{g}}$
Or $\frac{\Delta T}{T}=\frac{1}{2}\left(\frac{\Delta l}{l}-\frac{\Delta g}{g}\right)$
Or $\frac{\Delta g}{g}=\frac{\Delta l}{l}-\frac{2\Delta T}{T}$
$\therefore$ Maximum percentage error in $g$,
$\frac{\Delta g}{g}\times 100=\frac{\Delta l}{l}\times 100+\frac{2\Delta T}{T}\times 100$
$=1+2\times 2$
$=5$%