Mathematics

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

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 Answer: Option A
Explanation

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