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JEE Main 2025 (3 Apr, Shift 1) · Velocity of Efflux (Torricelli)

Velocity of Efflux (Torricelli) question from JEE Main 2025 (3 Apr, Shift 1)

Q8JEE Main 2025 · 3 APR · SHIFT 1Difficult

Velocity of Efflux (Torricelli)

Consider a completely full cylindrical water tank of height 1.6 m and of cross-sectional area 0.5 m20.5\text{ m}^2. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is:

(g=10 m/s2)(g = 10\text{ m/s}^2)

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Answer: (d)

  1. Extra pressure from load: P=mgA=50×100.5=1000 PaP = \frac{mg}{A} = \frac{50 \times 10}{0.5} = 1000\text{ Pa}
  2. Depth of hole: h=1.6−0.9=0.7 mh = 1.6 - 0.9 = 0.7\text{ m}
  3. Bernoulli: 12ρv2=ρgh+P⇒v2=2(10×0.7+10001000)=16\frac{1}{2}\rho v^2 = \rho g h + P \Rightarrow v^2 = 2\left(10 \times 0.7 + \frac{1000}{1000}\right) = 16
  4. So the answer is (d) v=4 m/sv = 4\text{ m/s}.
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