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...

We are told that the weight W of a metal bar varies jointly as its length L and the square of its diameter d, which can be expressed as:

W = kLd2

where k is a constant of variation. We need to find an expression for d in terms of W and L, given that W = 140 when d = 4/3 and L = 54.

To find the value of k, we can substitute the given values into the equation and solve for k as follows:

140 = k × 54 × (4/3)^2

140 = k × 54 × 16/9

k = 140 × 9 / (54 × 16)

k = 35 / 64

Now we can substitute the value of k into the original equation and solve for d in terms of W and L:

W = kLd2

d2 = W / (kL)

d = √(W / (kL))

Substituting the value of k, we get:

d = √((64/35) × W / L)

Simplifying, we get:

d = √((64W) / (35L))

Therefore, the expression for d in terms of W and L is:

d = √((64W) / (35L))

So the answer is option (A) √42W/5L.