A large open tank is filled with water to a…

A large open tank is filled with water to a depth of 5 m and stands on level ground. A small hole made in its side at a depth of 1 m below the free…

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A large open tank is filled with water to a depth of

5\ \mathrm{m}

and stands on level ground. A small hole made in its side at a depth of

1\ \mathrm{m}

below the free surface throws a horizontal jet that lands at some distance from the tank. A second small hole is made at a different depth so that its jet lands at the same distance. The depth of the second hole below the free surface is

A. $4\ \mathrm{m}$
B. $2.5\ \mathrm{m}$
C. $3\ \mathrm{m}$
D. $4.5\ \mathrm{m}$

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Answer: (A) $4\ \mathrm{m}$

By Torricelli's theorem the efflux speed at depth

h

\sqrt{2gh}

. The jet falls through a height

H - h

(with

H = 5\ \mathrm{m}

) in time

\sqrt{2(H-h)/g}

, so the range is

x = 2\sqrt{h(H-h)}

. For

h = 1\ \mathrm{m}

x = 2\sqrt{1\times4} = 4\ \mathrm{m}

. The same

x

requires

h'(H - h') = 4

, i.e.

h'^2 - 5h' + 4 = 0

, so

h' = 1\ \mathrm{m}

4\ \mathrm{m}

. The new hole is therefore at depth

4\ \mathrm{m}

, i.e.

1\ \mathrm{m}

above the ground. The depth

2.5\ \mathrm{m}

gives the maximum range,

5\ \mathrm{m}

, but not this one.

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Original question written in the JEE Main 2017 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake