The bulk modulus of a spherical object is . If it is subjected to uniform pressure , the fractional decrease in radius is [2017]

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Solution

Q.
The bulk modulus of a spherical object is $' B'$ . If it is subjected to uniform pressure $' p'$ , the fractional decrease in radius is [2017]

1 $\frac{B}{3 p}$

2 $\frac{3 p}{B}$

3 $\frac{p}{3 B}$

4 $\frac{p}{B}$

Ans.
(3)

Bulk modulus $B$ is given as

$B = \frac{- p V}{Δ V}$ ...(i)

The volume of a spherical object of radius $r$ is given as

$V = \frac{4}{3} π r^{3}, Δ V = \frac{4}{3} π (3 r^{2}) Δ r$

$∴$ $- \frac{V}{Δ V} = \frac{\frac{4}{3} π r^{3}}{\frac{4}{3} π 3 r^{2} Δ r} or - \frac{V}{Δ V} = - \frac{r}{3 Δ r}$

Put this value in eqn. (i), we get $B = - \frac{p r}{3 Δ r}$

Fractional decrease in radius is $- \frac{Δ r}{r} = \frac{p}{3 B}$

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