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JEE Advanced2015PhysicsGravitationActual

A bullet is fired vertically upwards with velocity υ from the surface of a spherical planet. When it reaches its maximum height, its acceleration due to the planet's gravity is 1 4 t h of its value at the surface of the planet. If the escape velocity from the planet is υ e s c = υ N , then the value of N is (ignore energy loss due to atmosphere)

Correct answer

0

Step-by-step solution

g ′ = g 1 + h R 2 = g 4 1 + h R = 2 h = R ...(i) So velocity of particle becomes zero at h = R Given v e s c = v N So 2 G M R = v N ...(ii) Applying conservation of energy - G M m R + 1 2 m v 2 = - G M m 2 R + 0 On solving v 2 = G M R So v = G M R putting in equation (ii) 2 G M R = v N Comparing N = 2

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