Question

A piece of stone of mass $113g$ sinks to the bottom in water contained in a measuring cylinder and water level in cylinder rises from $30ml$ to $40ml$. The relative density of stone is $X$. Find [$\frac{X}{4}$]. {where, [] is a step function}

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is C $2$

Mass of the stone $=113g$

Volume of stone = Volume of water displaced $=40ml-30ml=10ml$

Density of stone = $\frac{{Mass}_{stone}}{{Volume}_{stone}}$ = $\frac{113}{10}$ = $11.3g/ml$

Relative density of stone = $\frac{{density}_{stone}}{{density}_{water}}=11.3$

$x=11.3$

$\therefore \frac{x}{4}=\frac{11.3}{4}=2.825$

$\therefore \left[\frac{x}{4}\right]=2$