JEE MAIN - Physics (2007 - No. 32)
Angular momentum of the particle rotating with a central force is constant due to
constant torque
constant force
constant linear momentum
zero torque
Explanation
We know that $$\overrightarrow {{\tau _c}} = {{d\overrightarrow {{L_c}} } \over {dt}}$$
where $$\overrightarrow {{\tau _c}} $$ torque about the center of mass of the body and $$\overrightarrow {{L_c}} = $$ Angular momentum about the center of mass of the body.
Given that $$\overrightarrow {{L_c}} = $$ constant.
$$\therefore$$ $${{d\overrightarrow {{L_c}} } \over {dt}}$$ = 0
$$ \Rightarrow $$ $$\overrightarrow {{\tau _c}} = 0$$ [as $$\overrightarrow {{\tau _c}} = {{d\overrightarrow {{L_c}} } \over {dt}}$$]
where $$\overrightarrow {{\tau _c}} $$ torque about the center of mass of the body and $$\overrightarrow {{L_c}} = $$ Angular momentum about the center of mass of the body.
Given that $$\overrightarrow {{L_c}} = $$ constant.
$$\therefore$$ $${{d\overrightarrow {{L_c}} } \over {dt}}$$ = 0
$$ \Rightarrow $$ $$\overrightarrow {{\tau _c}} = 0$$ [as $$\overrightarrow {{\tau _c}} = {{d\overrightarrow {{L_c}} } \over {dt}}$$]
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