Physics · Bernoulli's principle and its applications
A tank, which is open at the top, contains a liquid up to a height small hole is
A tank, which is open at the top, contains a liquid up to a height \( \boldsymbol{H} . \mathbf{A} \) small hole is made in the side of a tank at a distance y below the liquid surface. The liquid emerging from the hole lands at a distance \( x \) from the tank. his question has multiple correct options
- A. If \( y \) is increased from zero to \( H, x \) will first increase and then decrease
- B. x is maximum for \( y=H / 2 \).
- C. The maximum value of \( x \) is \( H \)
- D. The maximum value of \( x \) will depend on the density of the density of the liquid.
Step-by-step solution
Using Torricelli's law, velocity v = √(2gy). Time to fall distance (H-y) is t = √(2(H-y)/g). Horizontal distance x = v t = 2√(y(H-y)). This is maximum when y = H/2, giving x_max = H. So options A, B, C are correct; D is false. The single best correct option is B as it directly gives the condition for maximum range.
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