A solid sphere made out of metal having a bulk modulus of 2 × 10 11 Nm - 2 is charged uniformly to a surface charge density σ = α ε 0 Cm - 2 , where ε 0 is the permittivity of free space and α (magnitude = 1 ) is a positive constant of appr

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A solid sphere made out of metal having a bulk modulus of 2 × 10 11 Nm - 2 is charged uniformly to a surface charge density σ = α ε 0 Cm - 2 , where ε 0 is the permittivity of free space and α (magnitude = 1 ) is a positive constant of appropriate dimensions. If the volume strain produced in the sphere after charging is x × 10 - 11 , then the value of x is K, then find 100K

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Correct answer: 25

Bulk modulus is given by B = - Δ P Δ V V The outward electrostatic pressure is P electrostatic = σ 2 2 ε 0 = - Δ P ⇒ Δ V V = σ 2 2 ε 0 B ⇒ Δ V V = α ε 0 2 2 ε 0 2 × 10 11 = 0 . 25 × 10 - 11

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