Final answer:
To determine the bulk modulus of elasticity of the sphere's material, calculate the sea pressure at 1 km depth and use the given volume contraction percentage to apply the bulk modulus formula. Option A is correct.
Step-by-step explanation:
The question involves finding the bulk modulus of elasticity of a material of a sphere that contracts by 0.01% when taken to the bottom of the sea 1 km deep. To solve this, we will use the definition of the bulk modulus, which is the ratio of the pressure increase (bulk stress) to the relative decrease in volume (bulk strain).
The pressure at 1 km depth in the sea is calculated as the product of the depth (h), the density of sea water (ρ), and acceleration due to gravity (g): P = hρg. Taking ρ as the typical seawater density of approximately 1025 kg/m³ and g as 9.80 m/s², the pressure P can be calculated.
Then, we apply the formula for bulk modulus: Bulk Modulus (K) = ΔP / (ΔV/V), where ΔP is the change in pressure, ΔV is the change in volume, and V is the original volume. Here, the change in volume (ΔV/V) is given as 0.01% or 0.0001 in decimal form.
Once we have calculated the pressure (P) and have the ΔV/V ratio, we can solve for the bulk modulus. The options provided suggest this will be on the order of 10¹¹ N/m².