Question

If a rubber ball is taken down to a 100 m deep lake, its volume decreases by 0.1%. If $g=10m/s^2$ then the bulk modulus of elasticity for rubber, in N/$m^2$, is

• A. ${10}^8$
• B. ${10}^9$
• C. ${10}^{11}$
• D. ${10}^{10}$

Answer 1

The correct option is D ${10}^{10}$

A rubber ball is taken 1 km depth inside
water
Pressure on rubber ball ,P = $P_0+\rho gh$
Here, Po is atmospheric pressure, p is
a density of water, g is acceleration due
to gravity and his depth inside water.
Given, h 1 km-1000 m
g 10 m/s2, $\rho$= 1000 kg/m3 density of
water

Now , pressure act on rubber ball , P = 1.03$\times {10}^5+1000\times 10\times 1000$
$1.03\times {10}^5+100\times {10}^5=101.03\times {10}^{5}N/m^2$
Given $\frac{\Delta V}{V}=\frac{0.05}{100}$

and$\Delta P$ =$P-P_o$ = ${10}^7$$N/m^2$

$\frac{\Delta V}{V}=5\times {10}^{-4}$

Now, bulk modulus = $\Delta P/\Delta V/V$

= $\frac{{10}^7}{5\times {10}^{-4}}$

= $2\times {10}^{10}N/m^2$