A solid sphere made out of metal having a bulk modulus of 2 × 10 ^...

Bulk modulus is given by

$B = \dfrac{- \DeltaP}{\dfrac{\DeltaV}{V}}$

The outward electrostatic pressure is

${P}_{electrostatic} = \dfrac{{\sigma}^{2}}{2{ε}_{0}} = - \DeltaP$

$⇒ \dfrac{\DeltaV}{V} = \dfrac{\dfrac{{\sigma}^{2}}{2{ε}_{0}}}{B}$

$⇒ \dfrac{\DeltaV}{V} = \dfrac{\dfrac{{\left(\sqrt{\alpha{ε}_{0}}\right)}^{2}}{2{ε}_{0}}}{2 \times {10}^{11}} = 0 . 25 \times {10}^{- 11}$