Question

Using screw gauge radius of wire was found to be $2.50\,mm$ . The length of wire found by mm Scale is $50.0\,cm$ . If the mass of the wire was measured as $25\,gm$, the density of the wire is correct S.F. will be $\left( {use\,\pi = 3.14\,exactly} \right)$ in $gm/c{m^3}$ .
A. $2.5$
B. $2.50$
C. $25$
D. $0.25$

Answer 1

As we know that density is defined as mass per unit volume. It is denoted by$\rho$. Density plays an important role in calculating mass and volume.
$V = m\rho$
Here, $V$ is volume,$m$is the mass and$\rho$the density.
$\rho$= $\dfrac{m}{V}$ ------- (1)
Volume of the wire can be given by- $V$=$\pi {r^2}l$
By substituting the volume and mass in equation (1), we can easily determine the value of density of the wire.Density is a scalar quantity because it does not show any direction.

Complete step by step answer:
Given that, radius of wire = 2.50$$$$mm= 2.50$$$$cm
Length of wire =50.0$$$$cm
Mass of wire = 25$$$$gm
Given, $\pi$=$3.14$
As we know that
$V = m\rho$
$\Rightarrow\rho$= $\dfrac{m}{V}$
$\Rightarrow\rho$= $\dfrac{{25}}{{\pi {r^2}l}}$
$\Rightarrow\rho$= $\dfrac{{25}}{{3.14 \times {{\left( {0.25} \right)}^2} \times 50.0}}$
$\therefore\rho = 2.5 \,gm/c{m^3}$

Hence, option A is correct.

Additional Information:
Volume is the amount of space occupied by a substance, while mass is the amount of matter.
Mass is physical value while volume is geometrical value. The SI unit of mass is $kg$and the SI unit of volume is ${m^3}$.

Note: Volume plays an important role in water conservation, and also when we fill up our vehicles at pumps. Density shows how much a substance occupies volume. The most common example of density is water and oil, when we mix oil and water. Oil is less dense than water so it floats. And a boat also floats on water because the density of the boat is less than water.