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Q.

A particle of charge q and mass m is subjected to an electric field  E=E0(1ax2)  in the x- direction , where a and  E0  are constants. Initially , the particle was at rest at x=0. other than the initial position , the kinetic energy of the particle becomes zero when the distance of the particle from the origin is

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a

3a

b

a

c

1a

d

2a

answer is C.

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Detailed Solution

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Here, Initial Kinetic energy ,

KI=0(at  x=0)

Final Kinetic energy 

Kf=0[atx=x0(say)]

So, charge in Kinetic energy 

Δk=kfkI=0

From work energy theorem Work done=change in Kinetic energy

i.e  W=Δk    W=0

Fdx=0qEdx=0   (F=Eq)

q[E0(1ax2)]dx=0   [E=E0(1ax2]

qE00x0(1ax2)dx=0

qE0(xax33]0x0=0

[{x0ax033}(00)]=0

x0ax033=0x0=ax0331=ax023

x02=3ax0=3a

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