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99 Percentile Qs Bank for JEE MainPhysicsGravitation

A tunnel has been dug through the centre of the earth and a ball is released in it. It will reach the other end of the tunnel after about

Options

  1. A42  minute 
  2. B84  minute 
  3. COne day
  4. DOne hour

Correct answer

A. 42  minute 

Step-by-step solution

Let A B be the imaginary tunnel dug through the centre of the earth. A ball is released from A in it. Consider that the density of earth be ρ and radius of earth be R . As the ball released, for half journey A O the acceleration due to gravity decreases. At a distance x from centre, F = G 4 3 π x ρ m ⇒  Acceleration  ∝ x The ball will execute SHM about the centre of the earth. The time taken to reach the other end = 1 2 × Time period of SHM t = 1 2 × 2 π  dis

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