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Question

A particle of mass and charge is released from rest in uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)


A
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B
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C
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D
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Solution

The correct option is B

Step1: Given data and assumptions.

Mass of the particle =m

Initial velocity u=0

Distance covered by the particle=x

Step 2: Find the acceleration of the particle.

We know that from newton's second law.

F=ma

Where F is the force, m is the mass of the particle, and a is the acceleration of the particle

a=Fm

Also,

Force F=Charge q×Electric field intensity E

Then,

a=qEm i

Step3: Finding the speed v on the distance x.

Formula used:

v2=u2+2as

Where v is the final velocity, a is the acceleration, s is the distance and u is the initial velocity.

Now,

v2=u2+2qEmx fromequationi

v2=0+2qEmx u=0

v2=2qEmx

Therefore v2=2qEmx represent the equation of the parabola.

Again,

v2=2qEmx

v=2qEmx

v=kx k=2qEm

vx

Thus from the above velocity-distance equation after assuming the value of distance x we get.

Hence, option B is correct.


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