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Electrostatics question

2019 · 8 Apr · Shift 1 · Q68
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Electrostatics question

2019 · 8 Apr · Shift 1 · Q68

JEE MainPhysicsElectrostaticsMCQ+4 / −1
The bob of a simple pendulum has mass 2g and a charge of 5.0 μC. It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equilibrium, the angle that the pendulum makes with the vertical is : (take g = 10 m/s2)
  1. A
    tan–1(5.0)
  2. B
    tan–1(2.0)
  3. C
    tan–1(0.5)
  4. D
    tan–1(0.2)
View written solutionFree

Correct answer: C

  1. Forces on the bob at equilibrium

    The bob is under three forces:

    • वजन: mgmgmg downward
    • Electric force: qEqEqE horizontal
    • Tension: along the string

    At equilibrium, the string makes an angle θ\thetaθ with the vertical, so tan⁡θ=horizontal forcevertical force=qEmg.\tan\theta = \frac{\text{horizontal force}}{\text{vertical force}} = \frac{qE}{mg}.tanθ=vertical forcehorizontal force​=mgqE​.

  2. Given data

    • Mass: m=2 g=2×10−3 kgm = 2\,\text{g} = 2 \times 10^{-3}\,\text{kg}m=2g=2×10−3kg
    • Charge: q=5.0 μC=5.0×10−6 Cq = 5.0\,\mu\text{C} = 5.0 \times 10^{-6}\,\text{C}q=5.0μC=5.0×10−6C
    • Electric field: E=2000 V/mE = 2000\,\text{V/m}E=2000V/m
    • g=10 m/s2g = 10\,\text{m/s}^2g=10m/s2

  3. Calculate electric force

    qE=(5.0×10−6)(2000)=1.0×10−2 N=0.01 N.qE = (5.0 \times 10^{-6})(2000) = 1.0 \times 10^{-2}\,\text{N} = 0.01\,\text{N}.qE=(5.0×10−6)(2000)=1.0×10−2N=0.01N.

  4. Calculate वजन

    mg=(2×10−3)(10)=2×10−2 N=0.02 N.mg = (2 \times 10^{-3})(10) = 2 \times 10^{-2}\,\text{N} = 0.02\,\text{N}.mg=(2×10−3)(10)=2×10−2N=0.02N.

  5. Find tan⁡θ\tan\thetatanθ

    tan⁡θ=qEmg=0.010.02=0.5.\tan\theta = \frac{qE}{mg} = \frac{0.01}{0.02} = 0.5.tanθ=mgqE​=0.020.01​=0.5.

    Therefore, θ=tan⁡−1(0.5).\theta = \tan^{-1}(0.5).θ=tan−1(0.5).

  6. Option check

    • A: tan⁡−1(5.0)\tan^{-1}(5.0)tan−1(5.0) ❌
    • B: tan⁡−1(2.0)\tan^{-1}(2.0)tan−1(2.0) ❌
    • C: tan⁡−1(0.5)\tan^{-1}(0.5)tan−1(0.5) ✅
    • D: tan⁡−1(0.2)\tan^{-1}(0.2)tan−1(0.2) ❌

Hence, the correct answer is Option C.

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