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JEE Main20241 Feb 2024Morning ShiftPhysicsGravitationActual

If R is the radius of the earth and the acceleration due to gravity on the surface of earth is g = π 2 m s - 2 , then the length of the second's pendulum at a height h = 2 R from the surface of earth will be:

Options

  1. A2 9 m
  2. B1 9 m
  3. C4 9 m
  4. D8 9 m

Correct answer

B. 1 9 m

Step-by-step solution

Acceleration due to gravity at the given height, g ' = G M 3 R 2 = 1 9 G M R 2 = 1 9 g , where g is acceleration due to gravity at the surface of the Earth. Now, time period is given by, T = 2 π l g ' Also the time period of second pendulum is 2 sec. Therefore, T = 2 sec Then, 2 = 2 π l g × 9 ⇒ l = 1 9 m

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