Q87 / 90 · JEE Main 2012 (26 May Online) · Physics

In a cylindrical water tank, there are two small holes $A$ and $B$ on the wall at a depth of $h_1$, from the surface of water and at a height of $h_2$ from the bottom of water tank. Surface of water is at height of $h_2$ from the bottom of water tank. Surface of water is at heigh $H$ from the bottom of water tank. Water coming out from both holes strikes the ground at the same point $S$. Find the ratio of $h_1$ and $h_2$ Figure

  • Correct answer
    A
    Depends on $H$
  • B
    $1: 1$
  • C
    $2: 2$
  • D
    $1: 2$

Solution

Range is same for both holes $$ \therefore 2 \sqrt{\left(\mathrm{H}-h_1\right) h_1}=2 \sqrt{\left(\mathrm{H}-h_2\right) h_2} $$ Squaring both sides, $$ \begin{aligned} & 4\left(H-h_1\right) \mathrm{h}_1=4\left(H-h_2\right) h_2 \\ & H h_1-h_1^2=H h_2-h_2^2 \end{aligned} $$ On solving we get, $$ H=h_1+h_2 $$ Hence, the ratio of $\frac{h_1}{h_2}$ depends on $H$.

Hence, the correct answer is option: 'A'.

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