A cylinder of height 1 ~m is filled with water. If a small orifice...

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 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

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

Options

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

Correct answer

D. $86.6 \mathrm{~cm}$

Step-by-step 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}

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