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

Options

A. the forces may be acting radiaally from a point on the axis
B. the forces may be acting on the axis of rotation
C. the forces may be acting parallel to the axis of the axis of rotation
D. the torque caused by some forces may be equal and opposite to that caused by other forces

Answer

a,b,c,d

Explanation

We know that torque on a system of particles `tau=rxxF sin theta hatn`
where`theta` is angle between r and F and `hatn` is a unit vector perpendicular to both r and F .
(a) when forces act radially ` theta `=0 hence `|tau|=0` [ from Eq (i)]
(b) when forces are acting on the axis of rotation ,`r=o,|tau|=0` [from Eq.(i)]
(c ) when forces acting parallel to the axis of rotation `theta =0^(@),|tau|=0` [from Eq.(i) ]
(d ) when torque by forces are equal and opposite `tau_("net")=yau_(1)-tau_(2)=0`