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JEE Main 202228 JulyEvening Shift
Exam
JEE Main
Year
2022
Date
28 July
Shift
Evening Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2022 · 28 July · Evening Shift · Physics · Gravitation

Assume there are two identical simple pendulum Clocks- 1 is placed...

Assume there are two identical simple pendulum Clocks-11 is placed on the earth and Clock-22 is placed on a space station located at a height h above the earth surface. Clock-11 and Clock-22 operate at time periods 4s4s and 6s6s respectively. Then the value of hh is -
(consider radius of earth RE=6400km{R}_{E} = 6400km and gg on earth 10ms−210m{s}^{- 2})

Options

  1. A1200km1200km
  2. B1600km1600km
  3. C3200km3200km
  4. D4800km4800km

Correct answer

C. 3200km3200km

Step-by-step solution

The time period of a simple pendulum is given by, T=2πlgT = 2\pi\sqrt{\dfrac{l}{g}}.

Therefore, T∝1gT ∝ \dfrac{1}{\sqrt{g}}.

The acceleration due to gravity at height hh from the surface of the earth is given by, g′=g(R+h)2{g}^{'} = \dfrac{g}{{\left(R + h\right)}^{2}}

Therefore,

T1T2=g2g1⇒46=RR+h⇒h=R2=3200km\dfrac{{T}_{1}}{{T}_{2}} = \sqrt{\dfrac{{g}_{2}}{{g}_{1}}} ⇒ \dfrac{4}{6} = \dfrac{R}{R + h} ⇒ h = \dfrac{R}{2} = 3200km

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