The weight W kg of a metal bar varies jointly a... - JAMB Mathematics 2005 Question
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.
A
\(\sqrt{\frac{42W}{5L}}\)
B
\(\sqrt{\frac{6L}{42W}}\)
C
\(\frac{42W}{5L}\)
D
\(\frac{5L}{42W}\)
correct option: a
\(W\infty LD^2\W=KLd^2\K=\frac{W}{Ld^2}\=\frac{140}{54}\times\left(4\frac{2}{3}\right)^2 \=\frac{140}{54}\times\left(\frac{14}{3}\right)^2\=\frac{140\times 9}{54\times 14\times 14}\=\frac{5}{42}\∴W=\frac{5}{42Ld^2}\42W=5Ld^2\\frac{42W}{5L}=d^2\d=\sqrt{\frac{42W}{5L}}\)
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