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Asked by eknathmote50 | 24 Jun, 2019, 11:21: AM
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Acceleration acting towards surface of imaginary planet is modified because there is an electric force in addition to gravitataional force.
 
Let a be the modified acceleration . 
 
Time taken T  by the ball to reach maximum height  is given by , T = v/a  ................(1)
where v is initial throwing speed of ball. 
 
If t is time to hit the ground after throwing the ball,  t = 2T = 2v/a  ....................(2)
 
net force acting on ball of mass m and charge q  :-   mg + qE = ma ...................(3)
 
where E is uniform electric field.  from (3) we write electric field E as,  E  = (m/q) [ a - g ] ..................(4)
 
If h is maximum height reached by the ball,  then we have,  h = v2/(2a)  .......................(5)
 
If V is potential difference beween planet surface and maximum height, then we have  V = E×h  ..........(6)
 
using eqn.(4) and (5), we rewrite eqn.(6) as ,    V = (m/q) [ a - g ] × [ v2/(2a) ]  .........................(7)
 
By using the substitution v/a = t/2 using eqn.(2),  eqn.(7) can be simplified as,  V = [ (mv)/(2q) ] × [ v - (gt/2) ]
Answered by Thiyagarajan K | 24 Jun, 2019, 13:24: PM

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