Question

A metallic cube of side 100 cm is subjected to a uniform force acting normal to the whole surface of the cube. The pressure is 106 pascal. If the volume changes by 1.5 * 10-5 m3 , calculate the bulk modulus of the material ​

Answer 1

Answer:

A metal cube of side 1 m is subjected to a uniform force acting normally on the whole surface of the cube, If the volume changes by 1.5×10

−5

m

2

and if the pressure is 10

6

Pa, find the bulk modulus of the metal.

Answer 2

Given:

$\text { Volume } \Delta v=1.5 \times 10^{-5} \mathrm{~m}^{3}$

$\text { pressure } P=10^{6}$

$V=100 \mathrm{~cm} \Rightarrow 1 \mathrm{~m}^{3}$

$\text { (given } \rightarrow \text { cube of side } 1 \mathrm{~m} \text { ) }$

$\begin{aligned}P=B \frac{\Delta v}{v} \\B=\frac{P}{\frac{\Delta V}{v}}=\frac{10^{6} \times 1}{1.5 \times 10^{-5}} &=0.667 \times 10^{11} \mathrm{N} / \mathrm{m}^{2} \\&=6.67 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}\end{aligned}$

The bulk modulus of the material ​$6.67 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$