Two small spheres having same mass and charge are loacated at the same vertical line at heights h₁ and h₂(h₂>h₁). They both are thrown simultaneously with the same velocity V in the same direction along the horizontal. From the initial vertical line, the first sphere hits the ground ata distance l. Then at this instance height of second ball,H=??

Ans in terms of h₁,h₂,l,V and g(acc due to gravity)

let mass of both the charges is m and charge on both the charges is q

take a sphere which is at height h1 two forces act on it

force of gravitation in downword direction and electrostatic force in downward direction hence net downward direction is qe+mg/m hence accelaration is qe/m+g hence

h1=1/2(g+qe/m)t^2

let t is time taken by small sphere in travelling distance

l=vt , t=l/v

let x is distance travelled by second sphere

forces acting on it

force of gravitation downward and electrostatic force upwards hence net acceleration in downward direction is( g-qe/m)

X=1/2(g-qe/m)t^2

height at this instant is h2-x

x=gl^2/v^2-h1

hence height is h2-(gl^2/v^2)