Question

In polar form the term, \(\frac{∂r}{∂y}\) is given by______

(a) \(\frac{∂r}{∂y}=sinθ\)

(b) \(\frac{∂r}{∂y}=cosθsinθ\)

(c) \(\frac{∂r}{∂y}=cosθ\)

(d) \(\frac{∂r}{∂y}=sin2θ\)

I had been asked this question during an interview for a job.

This interesting question is from Consolidation Equation in Polar Coordinates topic in chapter One Dimensional Consolidation of Geotechnical Engineering I

Answer 1

The correct answer is (a) \(\frac{∂r}{∂y}=sinθ\)

To explain I would say: Since we know, r^2=x^2+y^2 —————-(1)

∴ differentiating (1) with respect to y, we get,

\(\frac{∂r}{∂y}=\frac{y}{r}=\frac{rsinθ}{r}=sinθ.\)