Q. 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) $5\%$
Explanation
Time period of a simple pendulum is $T = 2\pi\sqrt{\frac{L}{g}}\ \Rightarrow g = \frac{4\pi^{2}L}{T^{2}}$ $\therefore\frac{\mathrm{\Delta}g}{g} \times 100 = \left( \frac{\mathrm{\Delta}L}{L} + 2\frac{\mathrm{\Delta}T}{T} \right) \times 100 = 1\% + 2 \times 2\% = 5\%$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.