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  • The net external torque on a system of particle about an axis is zero. Which of the following are compatible with it? a) the forces may be acting radially from a point on the axis b) the forces may be acting on the axis of rotation

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

a) the forces may be acting radially 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 rotation

d) the torque caused by some forces may be equal and opposite to that caused by other forces

Answers (1)

 

The correct answer is the option (a, b, c, d) Torque is given by \vec{\tau }=\vec{r}\times \vec{F}

                                                            Or

 \tau =rF \sin \theta \; \widehat{n}  where \theta is the angle between both the vectors and  \widehat{n} is the unit vector perpendicular to the plane of  \vec{r}and  \vec{F}

  1. When the force is acting radially in the direction of \vec{r}, \theta =0

                                                     \tau =rF\; \sin \; 0^{o}=0

  1. When the forces are acting on the axis of rotation then \theta =0 and thus \tau =0
  2. The component of forces in the plane of \vec{r}and  \vec{F}  when they are parallel to the axis of rotation is F\; \cos\; 90^{o} which is equal to 0. Hence \tau =0
  3. When torques are equal in magnitude but opposite in direction, the net resultant is 0.
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