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Physics Question on Modern Physics

Let (r, θ\theta) denote the polar coordinates of a particle moving in a plane. If r^\hat{r} and θ^\hat{\theta} represent the corresponding unit vectors, then

A

dr^dθ=θ^\frac{d\hat{r}}{d\theta}=\hat{\theta}

B

dr^dr=−θ^\frac{d\hat{r}}{dr}=-\hat{\theta}

C

dθ^dθ=−r^\frac{d\hat{\theta}}{d\theta}=-\hat{r}

D

dθ^dr=r^\frac{d\hat{\theta}}{dr}=\hat{r}

Answer

dr^dθ=θ^\frac{d\hat{r}}{d\theta}=\hat{\theta}

Explanation

Solution

The correct option is (A): dr^dθ=θ^\frac{d\hat{r}}{d\theta}=\hat{\theta} and (C): dθ^dθ=−r^\frac{d\hat{\theta}}{d\theta}=-\hat{r}