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JEE Main202228 Jul 2022Evening ShiftPhysicsGravitationActual

Assume there are two identical simple pendulum Clocks- 1 is placed on the earth and Clock- 2 is placed on a space station located at a height h above the earth surface. Clock- 1 and Clock- 2 operate at time periods 4 s and 6 s respectively. Then the value of h is - (consider radius of earth R E = 6400 km and g on earth 10 m s - 2 )

Options

  1. A1200   km
  2. B1600   km
  3. C3200   km
  4. D4800   km

Correct answer

C. 3200   km

Step-by-step solution

The time period of a simple pendulum is given by, T = 2 π l g . Therefore, T ∝ 1 g . The acceleration due to gravity at height h from the surface of the earth is given by, g ' = g R + h 2 Therefore, T 1 T 2 = g 2 g 1 ⇒ 4 6 = R R + h ⇒ h = R 2 = 3200   km

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