Kinematics

JEE Main level, single correct, medium

131 of 308

Question 131 of 308

A particle of charge qq and mass mm is subjected to an electric field E=E0(1–ax2)E={E}_{0}\left(1–a{x}^{2}\right) in the x−x-direction, where a and E0{E}_{0} are constants. Initially the particle was at rest at x=0x=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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Answer: (C) 3a\sqrt{\dfrac{3}{a}}

Wex=ΔKK1−K1=0{W}_{ex}=\Delta K{K}_{1}-{K}_{1}=0
∫0xqEdx=0{\int }_{0}^{x}qEdx=0
q∫0xE0(1−Qx2)dx=0\text{q}{\int }_{0}^{x}{E}_{0}\left(1-{Qx}^{2}\right)dx=0
qE0∫0x(1−ax2)dx=0{qE}_{0}{\int }_{0}^{x}\left(1-{ax}^{2}\right)dx=0
x−ax33=0x-\dfrac{{ax}^{3}}{3}=0
1−ax23=01-\dfrac{{ax}^{2}}{3}=0
ax23=1\dfrac{{ax}^{2}}{3}=1
x2=3a{x}^{2}=\dfrac{3}{a}
x=3ax=\sqrt{\dfrac{3}{a}}

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