A steel rod 55 cm long has a diameter of 30 cm.The compressive strength (the maximum stress it can support without breaking)of this steel is 500 × 10⁶ N/m².What is the compression force that would break the rod? A) 3.5 × 10⁷ N B) 2.4 × 10⁷ N C) 1.4 × 10⁸ N D) 4.7 × 10⁸ N E) 8.9 × 10⁸ N

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Quizplus · Accepted Answer

The compression force that would break the rod can be calculated by multiplying the compressive strength of the steel by the cross-sectional area of the rod. The area $A$ of the rod's cross-section, which is a circle, is given by $A = \pi r^2$, where $r$ is the radius of the rod. Given the diameter is 30 cm, the radius $r$ is 15 cm or 0.15 m. Thus, $A = \pi (0.15)^2 = 0.0706858 m^2$. The compressive strength is $500 \times 10^6 N/m^2$. Therefore, the maximum compression force $F$ is $F = 500 \times 10^6 N/m^2 \times 0.0706858 m^2 = 35.3429 \times 10^6 N = 3.5 \times 10^7 N$.

A Steel Rod 55 Cm Long Has a Diameter of 30