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JEE Advanced 2020Paper 1
Exam
JEE Advanced
Year
2020
Paper
Paper 1
Subject
Physics
Chapter
Motion in Two Dimensions

JEE Advanced 2020 · Paper 1 · Physics · Motion in Two Dimensions

A uniform electric field, → E = - 400 3 ^ j N C ^ - 1 is applied in...

A uniform electric field, \overset{\to}{E} = - 400\sqrt{3}\overset{^}{j}N{C}^{- 1} is applied in a region. A charged particle of mass mm carrying positive charge qq is projected in this region with an initial speed of 210×106ms−12\sqrt{10} \times {10}^{6}m{s}^{- 1}. This particle is aimed to hit a target TT, which is 5m5m away from its entry point into the field as shown schematically in the figure. Take qm=1010Ckg−1\dfrac{q}{m} = {10}^{10}C{kg}^{- 1}. Then

A uniform electric field, → E = - 400 3 ^ j N C ^ - 1 is applied in a region. A charged particle of mass m carrying

Options

  1. Athe particle will hit TT if projected at an angle 45°45 ° from the horizontal
  2. Bthe particle will hit TT if projected either at an angle 30°30 ° or 60°60 ° from the horizontal
  3. Ctime taken by the particle to hit TT could be 56\mus\sqrt{\dfrac{5}{6}}\mus as well as 52\mus\sqrt{\dfrac{5}{2}}\mus
  4. Dtime taken by the particle to hit TT is 53\mus\sqrt{\dfrac{5}{3}}\mus

Correct answer

B. the particle will hit TT if projected either at an angle 30°30 ° or 60°60 ° from the horizontal

Step-by-step solution

ay=EM=43×1012ms2{a}_{y} = \dfrac{E}{M} = 4\sqrt{3} \times {10}^{12}m{s}^{2}

A uniform electric field, → E = - 400 3 ^ j N C ^ - 1 is applied in a region. A charged particle of mass m carrying

R=u2sin⁡2θayR = \dfrac{{u}^{2}\sin 2\theta}{{a}_{y}}

sin⁡2θ=Rayu2=32\sin 2\theta = \dfrac{R{a}_{y}}{{u}^{2}} = \dfrac{\sqrt{3}}{2}

θ=30°\theta = 30 ° or 60°60 °

T=2usin30°ayT = \dfrac{2usin30 °}{{a}_{y}} or  2usin60°ay\dfrac{2usin60 °}{{a}_{y}}

=56\mus= \sqrt{\dfrac{5}{6}}\mus or 52\mus\sqrt{\dfrac{5}{2}}\mus

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