Question

A spherical ball contracts in volume by $0.01$ % when subjected to a normal uniform pressure of $100atm$. The Bulk modulus of its material is

• A. $1.01\times {10}^{11}N{m}^{-2}$
• B. $1.01\times {10}^{12}N{m}^{-2}$
• C. $1.01\times {10}^{10}N{m}^{-2}$
• D. $1.01\times {10}^{13}N{m}^{-2}$

Answer 1

The correct option is A $1.01\times {10}^{11}N{m}^{-2}$

Since the spherical contracts in volume by 0.01%

$\Rightarrow \frac{△v}{v}=\frac{0.01}{100}$

we know that

Bulk modulus 'B' is given by

$B=\frac{pressure\left(p\right)}{volumestrain\left(\frac{△v}{v}\right)}$

$\Rightarrow B=\frac{100\times 1.01\times {10}^5}{\frac{0.01}{100}}$

$\because$ 1atm $=1.01\times {10}^{5}N/m^2$

$\Rightarrow B=1.01\times {10}^{11}N{m}^{-2}$