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JEE Main202330 Jan 2023Evening ShiftPhysicsMotion in One DimensionActual

An object is allowed to fall from a height R above the earth, where R is the radius of earth. Its velocity when it strikes the earth’s surface, ignoring air resistance, will be :

Options

  1. A2 g R
  2. Bg R
  3. Cg R 2
  4. D2 g R

Correct answer

B. g R

Step-by-step solution

As gravitational field is a conservative field and therefore mechanical energy will be conserved. Therefore, Loss in PE = Gain in KE - G M m 2 R - - G M m R = 1 2 m v 2 ⇒ v 2 = G M R = g R as   g = G M R 2 ⇒ v = g R

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