A cube of metal is subjected to a hydrostatic pressure of $4\;GPa.$ The percentage change in the length of the side of the cube is close to.......$\%$
(Given bulk modulus of metal, $B =8 \times 10^{10}\, Pa$ )
(Given bulk modulus of metal, $B =8 \times 10^{10}\, Pa$ )
JEE MAIN 2020, Medium
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$B =-\frac{\Delta P }{\frac{\Delta V }{ V }}$
$\left|\frac{\Delta V }{ V }\right|=\frac{\Delta P }{ B }$
$=\frac{4 \times 10^{9}}{8 \times 10^{10}}=\frac{1}{20}$
$\frac{\Delta \ell}{\ell}=\frac{1}{3} \times \frac{\Delta V }{ V }=\frac{1}{60}$
Percentage change $=\frac{\Delta \ell}{\ell} \times 100 \%$
$=\frac{100}{60} \%=1.67 \%$
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