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JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

A simple pendulum is being used to determine the value of...

A simple pendulum is being used to determine the value of gravitational acceleration gg at a certain place. The length of the pendulum is 25.025.0 cm and a stopwatch with 1s1s resolution measures the time taken for 4040 oscillations to be 50s50s. The accuracy in~gg is:

Options

  1. A5.405.40%
  2. B3.403.40%
  3. C4.404.40%
  4. D2.402.40%

Correct answer

C. 4.404.40%

Step-by-step solution

Time period of the simple pendulum,& T=2πlg⇒g=4π2lT2T = 2\pi\sqrt{\dfrac{l}{g}} ⇒ g = \dfrac{4{π}^{2}l}{T2}

∆gg=2∆TT+∆LL⇒∆gg=2(150)+0.125.0\dfrac{∆ g}{g} = \dfrac{2 ∆ T}{T} + \dfrac{∆ L}{L} ⇒ \dfrac{∆ g}{g} = 2\left(\dfrac{1}{50}\right) + \dfrac{0.1}{25.0}

⇒∆gg=4.4⇒ \dfrac{∆ g}{g} = 4.4%

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