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JEE Main 2017 (9 Apr, Shift 1) · Viscosity & Stokes' Law

Viscosity & Stokes' Law question from JEE Main 2017 (9 Apr, Shift 1)

Q30JEE Main 2017 · 9 APR · SHIFT 1Medium

Viscosity & Stokes' Law

Two tubes of radii r1 and r2, and lengths l1 and l2, respectively, are connected in series and a liquid flows through each of them in stream line conditions. P1 and P2 are pressure differences across the two tubes.

If P2 is 4P1 and l2 is l14\frac{l_1}{4}, then the radius r2 will be equal to:

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Answer: (d)

  1. In series the same volume flows per second: Q=πPr48ηlQ = \frac{\pi P r^4}{8\eta l} is equal for both tubes.
  2. P1r14l1=P2r24l2=4P1r24l1/4=16P1r24l1\frac{P_1 r_1^4}{l_1} = \frac{P_2 r_2^4}{l_2} = \frac{4P_1 r_2^4}{l_1/4} = \frac{16P_1 r_2^4}{l_1}
  3. r24=r1416⇒r2=r12r_2^4 = \frac{r_1^4}{16} \Rightarrow r_2 = \frac{r_1}{2}
  4. So the answer is (d) r12\frac{r_1}{2}.
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