An ice-berg of density 900 kgm^ -3 is floating in water of density 1000 kgm^ -3 . The percentage of volume of ice-berg outside the water is

Correct answer: C. 10\% Let the volume of ice-berg is V and its density is . If this ice-berg floats in water with volume V_ in inside it then V_ in σ g=V g V_ in =(( )/(σ)) V aligned V_ out & =V-V_ in =((σ- )/(σ)) V & =((1000-900)/(1000)) V=(V)/(10) V_ out V & =0 · 1=10 \% aligned

JIPMER 2017

Exam: JIPMER
Year: 2017
Subject: Physics
Chapter: Mechanical Properties of Fluids

JIPMER 2017 · Physics · Mechanical Properties of Fluids

An ice-berg of density 900 kgm^ -3 is floating in water of density...

An ice-berg of density

900 \mathrm{kgm}^{-3}

is floating in water of density

1000 \mathrm{kgm}^{-3}

. The percentage of volume of ice-berg outside the water is

Options

A $20\%$
B $35\%$
C $10\%$
D $11\%$

Correct answer

C. $10\%$

Step-by-step solution

Let the volume of ice-berg is

V

and its density is

\rho

. If this ice-berg floats in water with volume

V_{\text{in }}

inside it then

V_{\text{in }} \sigma g=V \rho g \Rightarrow V_{\text{in }}=\left(\frac{\rho}{\sigma}\right) V

\begin{aligned} \Rightarrow V_{\text{out }} & =V-V_{\text{in }}=\left(\frac{\sigma-\rho}{\sigma}\right) V \\ & =\left(\frac{1000-900}{1000}\right) V=\frac{V}{10} \\ \Rightarrow \frac{V_{\text{out }}}{V} & =0 \cdot 1=10 \%\end{aligned}

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