The bulk modulus of a spherical object is B. If it is subjected to uniform pressure p, the fractional decrease in radius is

(a)$\frac{P}{B}$

(b) $\frac{B}{3p}$

(c) $\frac{3p}{B}$

(d)$\frac{p}{3B}$

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#5 | Bulk Modules & Shear Modules
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Concept Questions :-

Stress-strain

(d)The object is spherical and the bulk modulus is represented by B. It is the ratio of normal stress to the volumetric strain.

Hence             $B=\frac{F/A}{∆V/V}$

Hence p is applied pressure on the object and $\frac{∆V}{V}$ is

volume strain

Fractional decreasesin volume

Volume of the sphere decreases due to the decrease in its radius.

Hence $\frac{∆V}{V}=\frac{3∆R}{R}=\frac{P}{B}⇒\frac{∆R}{B}=\frac{P}{3B}$

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