Question

The weight Wkg of a metal bar varies jointly as it's length L and the square of it's diameter D mm. If W=140 when D =4 and L=54, find D interm of W and L

Answer 1

D =
`\sqrt{(216W)/(35L) }`

Explanation:

From the given question, the expression showing the relationship among the weight, length and diameter of the metal bar is;

W
`\alpha` L
`D^(2)`

W = kL
`D^(2)`

where k is the constant of proportionality.

When W = 140, D = 4 and L = 54, then;

140 = k(54)
`(4)^(2)`

= 864k

k =
`(140)/(864)`

=
`(35)/(216)`

k =
`(35)/(216)`

⇒ W =
`(35LD^(2) )/(216)`

So that;

35L
`D^(2)` = 216W

`D^(2)` =
`(216W)/(35L)`

D =
`\sqrt{(216W)/(35L) }`