Question

A rubber ball floats on water with its $1/3^{rd}$ volume outside water. The density of rubber is $Xkg{m}^{-3}$. Find $\left[\frac{3X}{1000}\right]$

(Take density of water $=1000kg{m}^{-3}$)

• A. $0.67$
• B. $1.5$
• C. $2$
• D. None of the above

Answer 1

Answer: (C)

$2$

$\frac{2}{3}$ of the volume of ball is inside water.
The rubber ball displaces $\frac{2}{3}$ of its volume of water, say , $\frac{2V}{3}$
Weight of ball = weight of water displaced.
= $\frac{2V}{3}\times$ density of water
Density of rubber = Mass /vol. = $\frac{2V}{3V}$ $\times$ density of water
= $\frac{2}{3}\times 1000=667kg{m}^{-3}$

$\left[\frac{3X}{1000}\right]=\left[\frac{3\times 667}{1000}\right]=2$