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  • The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'p', the fractional decrease in radius is :Option: 1</stron

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

Option: 1

\frac{\text{p}} {\text{B}}


Option: 2

\frac{\text{B}} {\text{3p}}


Option: 3

\frac{\text{3p}} {\text{B}}


Option: 4

\frac{\text{p}} {\text{3B}}


Answers (1)

best_answer

 

Bulk Modulus -

Ratio of normal stress to volumetric strain.

K=frac{f/A}{-Delta v/v}=frac{-Fv}{ADelta v}

K=frac{-Pv}{Delta v}

v = Original  volume

Delta v = Change in volume

P = Increase in pressure

-ve(sign) shows volume (Delta v) decrease.

- wherein

 

 Buck modulus is

B=-V\frac{\Delta P}{\Delta V}

or \frac{\Delta V}{V}=\frac{-\Delta P}{B}=-\frac{P}{B} -----(1)

V=\frac{4\pi}{3}r^{3} \: or \: \frac{dv}{v}=3\frac{dr}{r}

=3\left ( \frac{\Delta r}{r} \right )=-\frac{P}{B}

or

= \frac{-\Delta r}{r}=+\frac{P}{3B}

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