Question

A particle moves in a force field given by $\stackrel{-}{F}=\hat{r}{F}_r$ where $\hat{r}$ is a unit vector along the position vector $\stackrel{-}{r}$ with respect to O, then which of the following is true?

• A. The torque acting on the particle produces an angular acceleration in it
• B. The force acting on the particle produces a linear acceleration in it
• C. The angular momentum of the particle about O is conserved
• D. The linear momentum of the particle is not conserved

Answer 1

The correct option is C The angular momentum of the particle about O is conserved

Let us consider the Torque in this question,
Torque: $\tau =\overrightarrow{r}\times \overrightarrow{F}$
Since, $\overrightarrow{F}\parallel \overrightarrow{r}$ $\tau =0$
$\tau =\frac{dL}{dt}$
$\frac{dL}{dt}=0$, $\Rightarrow L=constant$
$\Rightarrow$ angular momentum of particle about O is conserved.