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 ^ th of its value at the surface of

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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 _ esc = v N So (2GM)/(R) = v N ...(ii) Applying conservation of energy (- GMm)/(R) + (1)/(2)m v ^ 2 = - (GMm)/(2R) + 0 On solving v ^ 2 = (GM)/(R) So v = (GM)/(R) putting in equation (ii) (2GM)/(R) = v N Comparing N = 2

A bullet is fired vertically upwards with velocity υ from the...

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