Question

When a rubber ball is taken to the bottom of a sea of depth $1400 \,m$, its volume decreases by $2 \%$. The Bulk modulus of rubber ball is [density of water is $1 \,g\, cc$ and $g=10 \,m / s ^{2}$ ]

• A. $7 \times 10^{8} N / m ^{2}$
• B. $6 \times 10^{8} N / m ^{2}$
• C. $14 \times 10^{8} N / m ^{2}$
• D. $9 \times 10^{6} N / m ^{2}$

Answer 1

Answer: (A)

Pressure at the bottom of sea $=\rho_{w} g h$
$=1000\, kg / m ^{3} \times 10\, m / s ^{2} \times 1400 \,m$
$ =14000000 \,N / m ^{2}$
Also we know
$\frac{\Delta V}{V}=-\frac{P}{B} $
$\left\{\frac{\Delta V}{V}=\frac{-2}{100}\right\}$
$\frac{-2}{100}=\frac{-14000000}{B} $
$B=7 \times 10^{8} N / m ^{2}$