Final answer:
The depth to which a rubber ball can be taken in a lake so that its volume is decreased by 0.1% is 100 m. Hence the correct answer is option D
Step-by-step explanation:
To calculate the depth to which a rubber ball can be taken in a lake so that its volume is decreased by 0.1%, we can use the concept of bulk modulus. The bulk modulus is defined as the ratio of the change in pressure to the fractional change in volume. In this case, we know the bulk modulus of rubber is 9.8 × 10^8 N/m. To calculate the depth, we can use the formula:
ΔP = B * (ΔV/V)
Where ΔP is the change in pressure, B is the bulk modulus, ΔV is the change in volume, and V is the original volume. Since we want the volume to decrease by 0.1%, ΔV/V is equal to -0.001. Plugging in the values, we can solve for ΔP:
ΔP = (9.8 × 10^8 N/m) * (-0.001) = -9.8 × 10^5 N/m^2
We can use the formula for pressure in a fluid:
ΔP = ρ * g * Δh
Where ΔP is the change in pressure, ρ is the density of water, g is the acceleration due to gravity, and Δh is the change in depth. We can rearrange the formula to solve for Δh:
Δh = ΔP / (ρ * g)
Substituting the values, we get:
Δh = (-9.8 × 10^5 N/m^2) / ((1000 kg/m^3) * (9.8 m/s^2)) = -0.1 m
Since depth cannot be negative, it means that the ball cannot be taken to a depth where its volume is decreased by 0.1%. Therefore, the correct answer is option d) 100 m.