Answer : The correct option is, (A) [tex]0.002010812m^3[/tex]
Solution : Given,
Volume of mercury at temperature [tex]20^oC[/tex] = [tex]0.002m^3[/tex]
As we know that the mercury is a liquid substance. So, we have to apply the volume of expansion of the liquid.
Formula used for the volume expansion of liquid :
[tex]V_{T}=v_{1}[1+\gamma (T_{2}-T_{1})][/tex]
or,
[tex]V_{2}=V_{1}[1+\gamma (T_{2}-T_{1})][/tex]
where,
[tex]V_{T}[/tex] = volume of liquid at temperature [tex]T^oC[/tex]
[tex]V_{1}[/tex] = volume of liquid at temperature [tex]20^oC[/tex]
[tex]V_{2}[/tex] = volume of liquid at temperature [tex]50^oC[/tex]
[tex]\gamma[/tex] = volume expansion coefficient of mercury at [tex]20^oC[/tex] is 0.00018 per centigrade (Standard value)
Now put all the given values in the above formula, we get the volume of mercury at [tex]50^oC[/tex].
[tex]V_{2}=0.002[1+0.00018(50-20)]=0.0020108m^3[/tex]
Therefore, the volume of mercury at [tex]50^oC[/tex] is, [tex]0.002010812m^3[/tex]
