The weight W kg of a metal bar varies jointly as its length L meters…

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Mathematics JAMB 2005

The weight W kg of a metal bar varies jointly as its length L meters and the square of its diameter d meters. If w = 140 when d = 42/3 and L = 54, find d in terms of W and L.

  • \(\sqrt{\frac{42W}{5L}}\) checkmark
  • \(\sqrt{\frac{6L}{42W}}\)
  • \(\frac{42W}{5L}\)
  • \(\frac{5L}{42W}\)

The correct answer is: A

Explanation

\(W\infty LD^2\\W=KLd^2\\K=\frac{W}{Ld^2}\\=\frac{140}{54}\times\left(4\frac{2}{3}\right)^2 \\=\frac{140}{54}\times\left(\frac{14}{3}\right)^2\\=\frac{140\times 9}{54\times 14\times 14}\\=\frac{5}{42}\\∴W=\frac{5}{42Ld^2}\\42W=5Ld^2\\\frac{42W}{5L}=d^2\\d=\sqrt{\frac{42W}{5L}}\)
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