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MHT CET 2025 (22 Apr, Shift 1) · Velocity of Efflux (Torricelli)

Velocity of Efflux (Torricelli) question from MHT CET 2025 (22 Apr, Shift 1)

Q6MHT CET 2025 · 22 APR · SHIFT 1Difficult

Velocity of Efflux (Torricelli)

There are two identical small holes on the opposite side of a tank containing full of a liquid. The tank is open at the top. The difference in height between the two holes is ' hh '. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to

Figure

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Answer: (d)

  1. Each jet pushes the tank back with thrust F=ρav2F = \rho a v^2, and v2=2gdv^2 = 2gd at depth dd.
  2. The two jets point in opposite directions, so Fnet=ρa(v22−v12)=ρa⋅2g(d2−d1)F_{net} = \rho a(v_2^2 - v_1^2) = \rho a \cdot 2g(d_2 - d_1)
  3. d2−d1=h⇒Fnet=2ρaghd_2 - d_1 = h \Rightarrow F_{net} = 2\rho a g h
  4. So the answer is (d) Fnet∝hF_{net} \propto h.
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