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99 Percentile Qs Bank for JEE MainPhysicsGravitation

From the pole of the earth, a body of mass m is imparted a velocity v₀ directed vertically up. If M is the mass of the earth, R its radius and g is the free-fall acceleration on its surface, then the height h to which the body will ascent is (neglect air resistance)

Options

  1. AR v₀^2 (2 g R-v₀^2 )
  2. BR v₀^2 2 g R
  3. CR
  4. DR v₀^2 (2 g R+v₀^2 )

Correct answer

A. R v₀^2 (2 g R-v₀^2 )

Step-by-step solution

If body moves up to height h , then by conservation of energy, we get gathered ( KE )= ( PE ) 0- 1 2 m v₀^2= -G M m R - (- G M m R+h ) v₀^2 2 G m = 1 R - 1 R+h R(R+h) h = 2 g R^2 v₀^2 h= R ( 2 g R v₀^2 -1 ) or h= R v₀^2 2 g R-v₀^2 gathered

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