Which of the following statements is correct?

Question

BlackTom AI · Accepted Answer

Question restatement: Which of the following statements is correct?

Option 1: 'The resultant hydrostatic force on an inclined submerged body will act through a point at the area centroid' This statement claims the line of action passes through the area centroid. For a plane surface under hydrostatic pressure, the resultant force is indeed equal to pressure at the centroid times the area, and its line of action is perpendicular to the surface and passes through the centroid of the surface. However, the wording can be interpreted as asserting only a geometric pass-through without clarifying the role of pressure variation with depth. Because the exact line of action is normal to the surface and passes through the centroid of the area, this option is partially correct but might be considered ambiguous if one expects explicit reference to the centroid in the context of a nonuniform pressure field. Overall, this statement is not entirely precise on the nature of the resultant force direction and its dependence on the pressure distribution.

Option 2: 'The parallel axis theorem is required to calculate the magnitude of the resultant force on an inclined surface' The parallel axis theorem relates moments of inertia about different axes, not the magnitude of hydrostatic resultant force. The magnitude is found from F = p_c A, where p_c is the pressure at the centroid. Therefore invoking the parallel axis theorem here is incorrect.

Option 3: 'The resultant hydrostatic force acting on an inclined submerged body can be calculated by considering the pressure at the area centroid' This is a correct description: for a plane surface, the resultant hydrostatic force equals the pressure evaluated at the centroid of the surface multiplied by the area (F = p_c A). The pressure varies linearly with depth, so using the centroid’s depth to determine p_c gives the total force.

Option 4: 'The resultant hydrostatic force on an inclined submerged body will only be a function of the area of the body' This statement ignores the variation of pressure with depth and the orientation of the surface. The actual force depends on both area and the distribution of pressure, which depends on the submerged depth of the surface, so this is false.

In summary, option 2 and option 4 are incorrect because they misstate the role of the parallel axis theorem and ignore depth-dependent pressure effects, respectively. Option 1 is close to a correct idea but lacks the explicit link to the pressure variation and centroid-based calculation, making it less precise. Option 3 correctly captures the standard result for a plane surface under hydrostatic pressure: F = p_c A, with p_c being the pressure at the area centroid, yielding the correct magnitude and a correct conceptual basis for the calculation.

Which of the following statements is correct? 单项选择题

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