On an imaginary planet the acceleration due to gravity is same as that on Earth but there is also a downward electric field that is uniform close to the planet's surface. A ball of mass m carryin

Question

On an imaginary planet the acceleration due to gravity is same as that on Earth but there is also a downward electric field that is uniform close to the planet's surface. A ball of mass m carrying a charge q is thrown upward at a speed v and hits the ground after an interval t. What is the magnitude of potential difference between the starting point and the top point of the trajectory?

TestHub · Accepted Answer

Net downward acceleration: a n e t ​ = g + m qE ​ ; time of flight t = a n e t ​ 2 v ​ ⇒ E = q m ​ ( t 2 v ​ − g ) . Rise time 2 t ​ : h = 2 v ​ × 2 t ​ = 4 v t ​ . Δ V = E h = q m ​ ( t 2 v ​ − g ) 4 v t ​ = 2 q m v ​ ( v − 2 g t ​ ) - (A)

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