Physics - W.E.P. Question with Solution | TestHub

(A) $\vec{F}=2r^3\hat{r}$: Purely radial. Conservative.

(B) $\vec{F}=-\frac{5}{r}\hat{r}$: Purely radial. Conservative.

$$\left(C\right)\vec{F}=\frac{3\vec{r}}{r^3}$$

$$\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}$$

$$r=\sqrt{x^2+y^2+z^2}$$

$$\vec{F}=\frac{3(x\hat{i}+y\hat{j}+z\hat{k})}{(x^2+y^2+z^2{)}^{3/2}}$$

$$\vec{F}=\frac{3}{r^2}\hat{r}(Conservative)$$

(D) $\vec{F}\propto (y\hat{i}+x\hat{j})$: This is not a radial force (the vector $y\hat{i}+x\hat{j}$ does not point away from the origin like $x\hat{i}+y\hat{j}$ does). Non-conservative.

Final Answer: A, B, C