The bulk modulus of a sphere is ′K′. If it is subjected to uniform pressure ′p′ then fractional decrease in its radius is
A
K3p
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B
3pK
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C
p3K
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D
pK
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Solution
The correct option is Cp3K Bulk modulus(K)=−PressureVolumetric strain ⇒K=−p(ΔVV) ∴K=−pVΔV...(i) Now volume of sphere is given by: V=43πr3 ⇒ΔV=43π×3r2×Δr...(ii) −VΔV=−43πr343π×3r2×Δr −VΔV=−r3Δr...(iii)
From Eq. (i) and (iii): K=−pr3Δr ⇒ Fractional decrease in the radius is represented as: −Δrr=p3K