The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it ?

The net external torque on a system of particles about an axis is zero

1.	The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it ?
Answer» theforces may be actingradiaallyfroma pointon theaxis theforces maybe actingon theaxisof rotation the forces maybeactingparallel to theaxisofthe axisofrotation thetorquecausedby someforces may be equalandoppositeto thatcausedbyother forces Solution :We knowthattorqueona systemof PARTICLES `tau=rxxF sin theta HATN` where`theta`is anglebetweenr andF and`hatn`is a UNIT vectorperpendicularto bothr and F . (a)whenforcesact radially` theta `=0hence`\|tau\|=0` [ fromEq (i)] (b)whenforcesareactingon theaxisofrotation,`r=o,\|tau\|=0` [fromEq.(i)] (c )whenforcesactingparallelto theaxisofrotation `theta =0^(@),\|tau\|=0` [from Eq.(i) ] (d )whentorqueby forces are equalandopposite `tau_("net")=yau_(1)-tau_(2)=0`