A cylinder of height 1 ~m is filled with water. If a small orifice is made at a height of 0.25 ~m from the ground, the horizontal range of water stream will be

Correct answer: (D) 86.6 ~cm. v=√(2 g h)=√(2 × 10 × 0.75)=√15 ~m ~s^-1 Horizontal range, R=√((2 h)/g) × √15=√((2 × 0.25 × 15)/10)=√(15/20)=√(3/4) =1.732/2=0.866 ~m=86.6 ~cm

Q127 / 180 · AIIMS 2019 (26 May) · Physics

A cylinder of height $1 \mathrm{~m}$ is filled with water. If a small orifice is made at a height of $0.25 \mathrm{~m}$ from the ground, the horizontal range of water stream will be

A
$46.5 \mathrm{~cm}$
B
$56.6 \mathrm{~cm}$
C
$76.6 \mathrm{~cm}$
Correct answer
D
$86.6 \mathrm{~cm}$

Solution

$v=\sqrt{2 g h}=\sqrt{2 \times 10 \times 0.75}=\sqrt{15} \mathrm{~m} \mathrm{~s}^{-1}$ Horizontal range, $\begin{aligned} & R=\sqrt{\frac{2 h}{g}} \times \sqrt{15}=\sqrt{\frac{2 \times 0.25 \times 15}{10}}=\sqrt{\frac{15}{20}}=\sqrt{\frac{3}{4}} \\ & =\frac{1.732}{2}=0.866 \mathrm{~m}=86.6 \mathrm{~cm}\end{aligned}$

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

A cylinder of height $1 \mathrm{~m}$ is filled with water. If a small orifice is made at a height of $0.25 \mathrm{~m}$ from the ground, the horizontal range of water stream will be

Solution

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