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JEE Main 20241 FebruaryMorning Shift
Exam
JEE Main
Year
2024
Date
1 February
Shift
Morning Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2024 · 1 February · Morning Shift · Physics · Gravitation

If R is the radius of the earth and the acceleration due to gravity...

If RR is the radius of the earth and the acceleration due to gravity on the surface of earth is g=π2ms−2g = {\pi}^{2}m{s}^{- 2}, then the length of the second's pendulum at a height h=2Rh = 2R from the surface of earth will be:

Options

  1. A29m\dfrac{2}{9}m
  2. B19m\dfrac{1}{9}m
  3. C49m\dfrac{4}{9}m
  4. D89m\dfrac{8}{9}m

Correct answer

B. 19m\dfrac{1}{9}m

Step-by-step solution

Acceleration due to gravity at the given height, g′=GM(3R)2=19GM(R)2=19gg ' = \dfrac{GM}{{\left(3R\right)}^{2}} = \dfrac{1}{9}\dfrac{GM}{{\left(R\right)}^{2}} = \dfrac{1}{9}g, where gg is acceleration due to gravity at the surface of the Earth.

Now, time period is given by, T=2πlg′T = 2\pi\sqrt{\dfrac{l}{g '}}

Also the time period of second pendulum is 22 sec.

Therefore, T=2secT = 2sec

Then, 2=2πlg×92 = 2\pi\sqrt{\dfrac{l}{g} \times 9}

⇒l=19m⇒ l = \dfrac{1}{9}m

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