Question

The relative density is X. Find [10 X] . {Where, [] is a step function}

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is D $3$

Relative density of a substance is the ratio of its density to the density of a reference substance.
$Relativedensityofthebody=\frac{Weightofthebodyinair}{Lossofweightinwater}$.
In this case,
Weight of sinker in water$=12.6gf$
Weight of sinker in water + cork in air $=13.7gf$
Weight of sinker and cork, both in water $=10.5gf$
Therefore,
Weight of cork in air$=13.7-12.6=1.1gf$
Weight of cork in wate$=10.5-12.6=-2.1gf$(Since cork floats in water, upthrust on it is more than its own weight as it is made to sink with the force of the sinker, hence weight of cork in water is -ve.)

$RDofthecork=\frac{Weightofthebodyinair}{Lossofweightinwater}$

$=\frac{1.1}{1.1-(-2.1)}=0.33$ = $X$

Hence, the answer $10X=3.3$.