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Question

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 C p3K
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

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