Question

A tank is filled with water of density $ 1\,g $ per $ cm^3 $ and oil of density $ 0.9\, g $ per $ cm^3 $ The height of water layer is $ 100 \,cm $ and of the oil layer is $ 400\,cm $ . If $ g = 980 \, cm/s^2 $ , then the velocity of efflux from an operating in the bottom of the tank is :

• A. $ \sqrt{900\times980} cm/s $
• B. $ \sqrt{1000\times980} cm/s $
• C. $ \sqrt{920\times980} cm/s $
• D. $ \sqrt{950\times980} cm/s $

Answer 1

Answer: (C)

Pressure at the bottom of tank must equal pressure due to water of height $h$.
Let $d_w$ and $d_o$ be the densities of water and oil,
then the pressure at the bottom of the tank
$ = h_w d_w g + h_0d_0 g$
Let this pressure be equivalent to pressure due
to water of height $h$. Then
$hd_w g = h_w d_w g + h_0 d_0 g$
$∴ h = h_w + \frac{ h_0 d_0}{d_w}$
$ = 100 +360 = 460 $
According to Toricelli’s theorem,
$v =\sqrt{2\, gh} =\sqrt{2\times980\times460} $
$=\sqrt{920\times 980}\, cm/ s$