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JEE Main 2023 (13 Apr, Shift 2) · Terminal Velocity

Terminal Velocity question from JEE Main 2023 (13 Apr, Shift 2)

Q35JEE Main 2023 · 13 APR · SHIFT 2Medium

Terminal Velocity

Given below are two statements: one is labelled as Assertion A\mathbf{A} and the other is labelled as Reason R\mathbf{R}

Assertion A: A spherical body of radius (5±0.1) mm(5 \pm 0.1)\text{ mm} having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is 4%4\%. Reason R: The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.

In the light of the above statements, choose the correct answer from the options given below

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Answer: (b)

  1. vt=2r2(σ−ρ)g9η⇒vt∝r2v_t = \dfrac{2r^2(\sigma - \rho)g}{9\eta} \Rightarrow v_t \propto r^2.
  2. Δvv×100=2×Δrr×100=2×0.15×100=4%\dfrac{\Delta v}{v}\times100 = 2\times\dfrac{\Delta r}{r}\times100 = 2\times\dfrac{0.1}{5}\times100 = 4\%, so A is true.
  3. R says vt∝1/rv_t \propto 1/r, but actually vt∝r2v_t \propto r^2, so R is false.
  4. So the answer is (b) A is true but R is false.
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