Question

If the force applied on a particle is zero then the quantities which are conserved are

• A. Only momentum
• B. Only angular momentum
• C. Momentum and angular momentum
• D. Only potential energy

Answer 1

Answer: (C)

Momentum and angular momentum

Given $\overrightarrow{F}=0$

But, $\overrightarrow{F}=\frac{d\overrightarrow{P}}{dt}$

$\Rightarrow \frac{d\overrightarrow{P}}{dt}=0$

$\Rightarrow \overrightarrow{P}=constant$

But, $\overrightarrow{\tau }=\frac{d\overrightarrow{L}}{dt}$

$\overrightarrow{r}\times \overrightarrow{F}=\frac{d\overrightarrow{L}}{dt}$

Since $\overrightarrow{F}=0$, $\frac{d\overrightarrow{L}}{dt}=\overrightarrow{r}\times 0=0$

$\Rightarrow \overrightarrow{L}=constant$