A ball falling in a lake of depth 400 m has a decrease of 0.2% in its volume at the bottom. The bulk modulus of the material of the ball is `("in Nm"^(-2) )`

Options

A. `9.8 xx 10^(9)`
B. `9.8 xx 10^(10)`
C. `1.96 xx 10^(10)`
D. `1.96 xx 10^(9)`

Answer

D

Explanation

Given, `h= 400 "m", (Delta V)/( V) = 0.2`
We know that the bulk modulus of the material
`B = (h rho g)/( ((Delta V)/( V) ) )`
`B = (400 xx 10^3 xx 9.8)/( (0.2)/(100))`
`B= (400 xx 10^3 xx 9.8 xx 100)/( 0.2)`
`B= 2000 xx 10^3 xx 9.8 xx 100`
`B~= 1.96 xx 10^9 "Nm"^(-2)`