The surface of a planet is found to be uniformly charged. When a particle of mass m and no charge is thrown at an angle from the surface of the planet, it has a parabolic trajectory as in projectile motion with horizontal range L. A particle of mass m and charge q, with the same initial conditions has a range L/2. The range of particle of mass m and charge 2q with the same initial conditions is-

Options

A. L
B. `L//2`
C. `L//3`
D. `L//4`

Answer

C

Explanation

For uncharged particle
`L = (u^2 sin 2 theta)/g " "...(i)`
Range for particle of mass m and charge q
`L/2 =(u^2 sin2theta)/(g+(qE)/m)" "....(ii)`
From (i) and (ii)
`(u^2sin2theta)/(2g)=(u^2sin2theta)/(g+(qE)/m)implies mg =qE`
Range of particle of mass m and charge 2q
`implies R=(u^2sin2theta)/(g+(2qE)/m)=(u^2 sin2theta)/(g(1+(2qE)/(mg)))=L/3`