Question

If the atmospheric pressure is 76 cm of Hg at what depth of water the pressure will becomes 2 atmospheres nearly.

• A. $826cm$
• B. $932cm$
• C. $982cm$
• D. $1033cm$

Answer 1

The correct option is D $1033cm$

Let required depth be $h$

Pressure at that depth $=2$ atmosphere $=2\times 76cm$ of $Hg$

Pressure is due to atmosphere $+$ Pressure due to column of water $=2\times 76cm$ of $Hg$

$⟹76cm$ of $Hg+$ depth $\times$ density of water

$h\times d\times g=2\times 76cm$ of $Hg$

Or

$h\times d\times g=76cm$ of $Hg$

Or

$h=\frac{76cm\times 13\times g}{1000\times g}$ ( Note: pressure due to $h$ meter of $Hg=h\times$ density of mercury $\times g$)

Cancelling $g$ we have $h=13.6\times 76=1033.6cm$ ( as $cm$ is taken for atmosphere answer too comes in $cm$).