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

  • Option 1)

    \frac{B}{3p}

  • Option 2)

    \frac{3p}{B}

  • Option 3)

    \frac{p}{3B}

  • Option 4)

    \frac{p}{B}

 

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

 

 B = -\frac{PV}{\Delta V}

V = \frac{-PV}{\Delta V}\Rightarrow \Delta V= \frac{4}{3}\pi (3r^{2})\Delta r

\therefore - \frac{V}{\Delta V} = \frac{\frac{4}{3}\pi r^{3} }{\frac{4}{3}\pi 3r^{2}\Delta r} or \frac{-V}{\Delta V} = \frac{-r}{3\Delta r}

Put this value in equation (i) we get

B= \frac{-Pr}{3\Delta r}

fractional decrease in radius is

\frac{-\Delta r}{r}=\frac{p}{3B}


Option 1)

\frac{B}{3p}

This solution is incorrect

Option 2)

\frac{3p}{B}

This solution is incorrect

Option 3)

\frac{p}{3B}

This solution is correct

Option 4)

\frac{p}{B}

This solution is incorrect

Posted by

Aadil

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