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AP EAMCET202123 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

The time period T of a simple pendulum of length l is given by T=2 l g , where g denotes the acceleration due to gravity. If the length of the pendulum is increased by 1 % , then the approximate change in its time period is

Options

  1. A0.5 %
  2. B2 %
  3. C1 %
  4. D4 %

Correct answer

A. 0.5 %

Step-by-step solution

Given, T=2 l g Then, d T d l = 2 g 1 2 l = T l 1 2 l [ T= 2 g l ] aligned d T d l = T 2 l & d T T = 1 2 d l l Given, d l l 100 & =1 d l l = 1 100 d T T & = 1 2 1 100 d T T 100 & = 1 2 1 100 100= 1 2 =0.5 % aligned Change in its time period T is 0.5 % .

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