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JEE Main201910 Apr 2019Morning ShiftPhysicsGravitationActual

The value of acceleration due to gravity at Earth's surface is 9.8 m s - 2 . The altitude above its surface at which the acceleration due to gravity decreases to 4.9 m s - 2 , is close to: (Radius of earth = 6.4 × 10 6 m )

Options

  1. A1.6 × 10 6 m
  2. B2.6 × 10 6 m
  3. C6.4 × 10 6 m
  4. D9.0 × 10 6 m

Correct answer

B. 2.6 × 10 6 m

Step-by-step solution

Acceleration due to gravity g = G M R 2 .......(1) ⇒ g 2 = G M ( R + h ) 2 ............(2) From (1) and (2), G M 2 R 2 = G M ( R + h ) 2 R + h = 2 R h = 0.414 × 6.4 × 10 6 = 2.6 × 10 6 m

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