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JEE Main 2021 · Physics · Fluid Mechanics, Elasticity and Surface Tension · medium

A tall vertical cylindrical tank is filled with water to a depth of 10 m. Two small holes are made in its side, and the jets from both strike the…

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A tall vertical cylindrical tank is filled with water to a depth of 10 m10\ \mathrm{m}. Two small holes are made in its side, and the jets from both strike the ground at the same point. The upper hole is 2 m2\ \mathrm{m} below the water surface. The height of the other hole above the base of the tank is
  1. A. 4 m4\ \mathrm{m}
  2. B. 2 m2\ \mathrm{m}
  3. C. 5 m5\ \mathrm{m}
  4. D. 6 m6\ \mathrm{m}
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Answer: (B) 2 m2\ \mathrm{m}

For a hole at depth hh below the surface, speed v=2ghv=\sqrt{2gh} and fall height H−hH-h (tank resting on the ground), so range x=2h(H−h)x=2\sqrt{h(H-h)}. Equal ranges need h1(H−h1)=h2(H−h2)h_1(H-h_1)=h_2(H-h_2), i.e. h2=H−h1=10−2=8 mh_2=H-h_1=10-2=8\ \mathrm{m} below the surface. Its height above the base is 10−8=2 m10-8=2\ \mathrm{m}.
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