Question

Compute the torque about the origin of the gravitational force F--mgj acting on a particle of mass m located at 7-xî+ yj and show that this torque is independent of the;y coordinate.

Answer 1

Answer:

Explanation:

Force, F = - mg j

r = - 7x i + y j

Torque is defined as the product f force and the perpendicular distance.

It is also defined as the cross product of force vector and the displacement vector.

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$

$\overrightarrow{\tau }=(- 7 x i + yj)\times (-mgj)$

[tex]\overrightarrow{\tau  }= 7 m g x k

Here, we observe that the torque is independent of y coordinate.