Final answer:
To find the compressive strength of the cylindrical rock sample, we calculate the area of its cross-section and then divide the load by this area. Using the formula for stress, we determine that the compressive strength is approximately 49.89 MPa, and rounded to the nearest ten, it is 50 MPa, which corresponds to answer C) 50 MPa.
Step-by-step explanation:
To calculate the compressive strength of a cylindrical rock sample with a diameter of 50mm that fails under a vertical compressive load of 98kN, you need to determine the cross-sectional area of the cylinder and then use the formula for stress, which is the force divided by the area.
First, calculate the radius (r) of the cylinder in meters (since 1m = 1000mm, r = 50mm / 2 / 1000 = 0.025m). Then, calculate the area (A) using the formula πr². A = π(0.025m)² = π(0.000625m²) ≈ 0.0019635 m².
Now, convert the compressive load from kN to N (1 kN = 1000 N), so the load (F) is 98kN = 98000N. The compressive strength (σ) is calculated using the formula σ = F/A. σ = 98000N / 0.0019635 m² ≈ 49893.97 Pa or ≈ 49.89 MPa when rounded to two decimal places.
Therefore, the correct answer is C) 50 MPa.