A large open tank, kept filled to a…

A large open tank, kept filled to a constant depth H=1.0 m with water, stands on level ground. A small hole is made in its vertical wall at a depth h…

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A large open tank, kept filled to a constant depth

H=1.0\ \mathrm{m}

with water, stands on level ground. A small hole is made in its vertical wall at a depth

h

below the water surface and the water jet strikes the ground at horizontal distance

x

from the wall. Take

g=10\ \mathrm{m\,s^{-2}}

. Choose the correct statement(s).

A. Holes at depths $0.2\ \mathrm{m}$ and $0.8\ \mathrm{m}$ give the same horizontal range.
B. The range is maximum for a hole at depth $\tfrac13\ \mathrm{m}$ .
C. The maximum possible horizontal range is $0.5\ \mathrm{m}$ .
D. The speed of efflux of the jet which has the maximum range is $4.47\ \mathrm{m\,s^{-1}}$ .

Show answer and solution

Answer: A

The efflux speed is

v=\sqrt{2gh}

(Torricelli) and the fall height is

H-h

, so the time of flight is

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

. The range is

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

, independent of

g

. (A) For

h=0.2

and

h=0.8

the product

h(H-h)=0.16

in both cases, so

x=0.8\ \mathrm{m}

: true. (B)

h(H-h)

is maximum at

h=H/2=0.5\ \mathrm{m}

, not at

\tfrac13\ \mathrm{m}

(where

x=0.94\ \mathrm{m}

): false. (C) The maximum range is

2\sqrt{0.25}=1.0\ \mathrm{m}

, not

0.5\ \mathrm{m}

: false. (D) For

h=0.5\ \mathrm{m}

v=\sqrt{2\times10\times0.5}=3.16\ \mathrm{m\,s^{-1}}

;

4.47\ \mathrm{m\,s^{-1}}

would be the speed at the full depth: false.

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Original question written in the JEE Advanced 2017 Paper 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake