KVPY SB SX Exam 2011 Question Paper

Question : 92 of 120

Marks: +1, -0

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

Validate

Solution:

For uncharged particle

L={u^2\sin2θ}/g

… (i)
Range for particle of mass m and charge q.

L/2={u^2\sin2θ}/{g+{qE}/m}

…. (ii)
From (i) and (ii)

{u^2\sin 2θ}/{2g}={u^2\sin2θ}/{g+{qE}/m}

⇒ mg = qE
Range of particle of mass m & charge 2q.

R={u^2\sin2θ}/{g+{2 qE}/m}

={u^2\sin 2θ}/{g(1+{2qE}/{mg})}=L/3

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