Question

The relative density of lead is 11.3. Its density in SI unit is then
(A). $1.13\times { 10 }^{ 3 }$
(B). $1.13\times { 10 }^{ 2 }$
(C). $1.13\times { 10 }^{ 4 }$
(D). $11.3$

Answer 1

Hint: In order to solve this question, you should have the basic idea of relative density. Relative density is defined as the ratio of the mass of the substance to the mass of water having equal volume at $4°C$. Relative density is also defined as the ratio of density of the substance to the density of water which is reference material. Use this formula to find relative density. Substitute the given values in the formula and calculate the density of lead.

Complete step-by-step answer:
Given: Relative density of lead = 11.3
Relative Density is given by,
$Relative\quad density=\dfrac { Density\quad of\quad a\quad substance }{ Density\quad of\quad water }$ …(1)
We know,
Density of water is $1\times { 10 }^{ 3 }{ kg }/{ { m }^{ -3 } }$
Now, substituting values in equation we get,
$11.3=\dfrac { Density\quad of\quad lead }{ 1\times { 10 }^{ 3 } }$
$\Rightarrow Density\quad of\quad lead=11.3\times 1\times { 10 }^{ 3 }$
$\Rightarrow Density\quad of\quad lead=11.3\times { 10 }^{ 3 }$
$\Rightarrow Density\quad of\quad lead=1.13\times { 10 }^{ 4 }$
Thus, density of lead in S.I. unit is $1.13\times { 10 }^{ 4 }{ kg }/{ { m }^{ -3 } }.$
Hence, the correct answer is option C i.e. $1.13\times { 10 }^{ 4 }.$

Note: Do not get confused between the terms relative density and density of a substance. Relative density is also called the specific density of the material. So, if instead of relative density, specific density is mentioned, don’t get confused. Relative density is the ratio of the same quantities. Hence, relative density has no unit. The density of water changes with the change in temperature. Thus, temperature is dependent on temperature.