Calculate the torque (magnitude and direction) about point `O` due to the forces as shown. In each case, forces and rod lie in the plane of the paper.
(`a`)
(`b`)
(`c` )
(`d`)

Explanation

Torque= force `xx` perpendicular distance from `O`
If the body rotates clockwise, torque is inside the plane of the paper and if the body rotates anticlockwise, torque is outside the plane of paper.
Anticlockwise torque is considered positive.
(`a`)
`tau_(0)=10xx3=30 Nm`, rod rotates clockwise
Torque is inside the plane of paper.
(`b`)
The force `10 cos 37^(@)` produces no torque, as it is passing through `O`.
`tau_(0)=10sin37^(@)xx3=10xx(3)/(5)xx3=18 Nm`, the rod rotates anticlockwise.
Torque is outside the plane of paper.
(`c`)
`5 N` and `10 sin 37^(@)`, both rotate the rod anticlockwise.
`tau_(0)=5xx1+10sin37^(@)xx3`
`=5xx1+10xx(3)/(5)xx3=23 Nm`
Torque is outside the plane of paper.
(`d`)
`10 N` produces no torque, `5 N` rotates the rod anticlockwise.
`10sin37^(@)` rotates the rod clockwise.
`tau_(0)=5xx1-10sin37^(@)xx2`
`=5-10xx(3)/(5)xx2=5-12=-7 Nm`
Negative sign, i.e. the rod rotates clockwise.
Torque is inside the plane of paper.