Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
If there is an error of in measuring the length of a simple pendulum, then perce
If there is an error of \( 2 \% \) in measuring the length of a simple pendulum, then percentage error in its period is
- A. \( 1 \% \)
- B. 2\%
- C. 3 \% \)
- D. \( 4 \% \)
Step-by-step solution
The period T of a simple pendulum is given by T = 2π√(L/g). Taking natural log: ln T = ln(2π) + (1/2) ln L - (1/2) ln g. Differentiating: dT/T = (1/2) dL/L. Thus percentage error in T is half of percentage error in L. Given error in L is 2%, so error in T = 1%.
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