ACT (Enhanced)MathematicsMedium
A civil engineer is designing a new bridge. The maximum allowable stress (S) on a support cable is inversely proportional to the square of its length (L). If a 10-meter cable can withstand a stress of 200 MPa, what stress can a 20-meter cable withstand?
- A25 MPa
- B400 MPa
- C50 MPa
- D100 MPa
Show answer & explanationAnswer & explanation
Correct answer: C. 50 MPa
Inversely proportional to the square means S = k/L^2. First, find k using the given values: 200 = k / (10^2) => 200 = k / 100 => k = 20000. Now use k to find the stress for L=20m: S = 20000 / (20^2) = 20000 / 400 = 50 MPa.
Why the other options are wrong
- A. Incorrect calculation. (200 * (10/20)^2 = 200 * 1/4 = 50. This is the correct method.)
- B. This would be if it were directly proportional to L^2.
- D. This would be if it were inversely proportional to L, not L^2.
Inverse Square Proportionality
One quantity is inversely proportional to the square of another if their product (with the second quantity squared) is a constant. As one increases, the other decreases rapidly.
- Represented by y = k/x^2, where k is the constant.
- If x doubles, y becomes one-fourth of its original value.
- Common in physics (e.g., gravity, light intensity).
Memory trick: Inverse 'I'nvolves 'I'nverse 'I'ncreases, 'I'f you 'I'nvert and 'I'nclude the square.