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Solution for 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% - CBSE (Science) Class 12 - Mathematics

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Question

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%

Solution

(a) 1%
Let l be the length if the pendulum and T be the period.

\[\text { Also, let ∆ l be the error in the length and ∆ T be the error in the period } . \]

\[\text { We have }\]

\[\frac{∆ l}{l} \times 100 = 2\]

\[ \Rightarrow \frac{dl}{l} \times 100 = 2\]

\[\text { Now,} T = 2\pi\sqrt{\frac{l}{g}}\]

\[\text { Taking \log on both sides, we get }\]

\[\log T = \log 2\pi + \frac{1}{2}\log l - \frac{1}{2}\log g\]

\[\text { Differentiating both sides w . r . t . x, we get }\]

\[\frac{1}{T}\frac{dT}{dl} = \frac{1}{2l}\]

\[ \Rightarrow \frac{dT}{dl} = \frac{T}{2l}\]

\[ \Rightarrow \frac{dl}{l} \times 100 = 2\frac{dT}{T} \times 100\]

\[ \Rightarrow \frac{dT}{T} \times 100 = \frac{2}{2}\]

\[ \Rightarrow \frac{∆ T}{T} \times 100 = 1\]

\[\text { Hence, there is an error of 1 % in calculating the period of the pendulum } .\]

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APPEARS IN

 RD Sharma Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (with solutions)
Chapter 14: Differentials, Errors and Approximations
Q: 1 | Page no. 13

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Solution for question: 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% concept: Approximations. For the courses CBSE (Science), CBSE (Commerce), PUC Karnataka Science, CBSE (Arts)
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