Question

The bulk modulus of rubber is to what depth a rubber ball be taken in a lake so that its volume is decreased by 0.1%? Options

Answer 1

your question is incomplete. A complete question is ----> To what depth must a rubber ball be taken in deep sea so that its volume is decreased by 0.1%. (The bulk modulus of rubber is 9.8 x 10^8 N/m²; and the density of sea water is 10³ kg/m³)

solution : first of all,

applying bulk modulus formula,

i.e., bulk modulus , $\beta=\frac{\Delta P}{\frac{\Delta V}{V}}$

given, percentage decrease in volume = 0.1%

so, ∆V/V × 100 = 0.1%

or, ∆V/V = 0.001 = 10^-3

and $\beta=9.8\times10^8$ N/m²

so, 9.8 × 10^8 = ∆P/10^-3

or, ∆P = 9.8 × 10^5 N/m²

we know, ∆P = $\rho gh$

where, $\rho$ is density of sea water, g is acceleration due to gravity and h is depth of rubber ball.

here, ∆P = 9.8 × 10^5 N/m², $\rho$ = 10³ kg/m³ and g = 9.8 m/s²

so, h = ∆P/$\rho g$

= 9.8 × 10^5/(10³ × 9.8)

= 100 m

hence, answer is 100m

Answer 2

Your q is incomplete....

U must provide us the valueof bulk modulous...

find pressure by formula = density * g * height

and bulk modulous = p * v/Δv