A force `vec(F) = (hati + 3 hatj) N` acts on a body at a point P , which is at a distance , give by `vec(r) = (3hati + hatj)` m form the axis of rotation .
What is the direction of the torque acting on the body ?

Options

A. Positive X axis
B. Positive Y axis
C. Positive Z axis
D. Negative Z axis

Answer

C

Explanation

`hati xx hati = hatj xx hatj =`
`hati xx hatj = hatk and hatj xx hati = - hatk`
Torque `(tau) = vec(r) xx vec(F)`
` = (3hati + hatj) xx (hati + 3hatj)`
` = 3hati xx hati + 3hati xx 3hatj + hatj xx hati + hatj xx 3hatj`
` = 0 + 9 hatk - hatk + 0 = 8hatk`
` therefore vec(tau) = 8 hatk`
`therefore ` The magnitude of the torque = 8 N -m and the direction of the torque is along the positive direction of the Z axis.