Question

Statement-1 : The net linear momentum of a system of two moving particles is zero. Then at a particular instant of time, the net angular momentum of system of given two particles is same about any point.
Statement-2 : If net linear momentum of a system of two moving particles is zero, then angular momentum of system of given two particles is zero about any point.

• A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
• B. Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1
• C. Statement-1 is True, Statement-2 is False
• D. Statement-1 is False, Statement-2 is True.

Answer 1

Answer: (C)

Statement-1 is True, Statement-2 is False

$\overrightarrow{L_1}=$$\overrightarrow{r_1}$ x $\overrightarrow{p_1}$
$\overrightarrow{L_2}=$$\overrightarrow{r_2}$ x $\overrightarrow{p_2}$
Given, $\overrightarrow{p_1}+\overrightarrow{p_2}=0$
$\overrightarrow{L}=\overrightarrow{L_1}+\overrightarrow{L_2}=\overrightarrow{r_1}\times \overrightarrow{p_1}+\overrightarrow{r_2}\times \overrightarrow{p_2}=\overrightarrow{r_1}\times (-\overrightarrow{p_2})+\overrightarrow{r_2}\times \overrightarrow{p_2}=(\overrightarrow{r_2}-\overrightarrow{r_1})\times \overrightarrow{p_2}=\overrightarrow{r_{rel}}\times \overrightarrow{p_2}$
Statement-2 : If net momentum of a system of two moving particles is zero, then angular momentum of system of given two particles is zero about any point. Net angular momentum is non zero.
Statement-1 : The net momentum of a system of two moving particles is zero. Then at a particular instant of time, the net angular momentum of system of given two particles is same about any point.
Since net angular momentum depends on relative position coordinates and momentum of 2nd particle, it is same about any point because $r_{rel}$ will remain same and $\overrightarrow{p_2}$ is constant.