Question

Given that force (5i + 7j - 3k) N acts on a particle at position (i+ j - k) m. Find torque of this force on the particle about origin.
A) 4i-2j+2k
B) 2i-3j+4k
C) 5i-2j+3k
D) 6i-4j+4k

Answer 1

Hint: The torque acting on anybody is the cross product of position of the particle and the force acting on the particle at any instant. So, what we need to do is to apply the cross product between the force and position that is given to us.
Formula used:
$\tau =r\times F$

Complete answer:
The torque acting is the cross product of the position of the body and the force acting on the object. Now, the position and the force acting on the object is given,
Therefore, the cross product will be,
$\begin{align}
  & \tau =r\times F \\
 & \Rightarrow \tau =(i+j-k)\times (5i+7j-3k) \\
 & \Rightarrow \tau =i(-3+7)-j(-3+5)+k(7-5) \\
 & \Rightarrow \tau =4i-2j+2k \\
\end{align}$

So, the correct answer is “Option A”.

Additional Information:
Torque is the measure of force that can cause an object to rotate about an axis. Force is what causes an object to accelerate in linear kinematics similarly, torque’s what causes an angular acceleration. We can define torc as the rotational equivalent of linear force. The point where the object rotates is called the axis of rotation. In physics, torque is simply the tendency of efforts to turn or twist. Torque can be either static or dynamic. Static torque doesn’t produce any angular acceleration in the system. An example of a person pushing the closed door is applying static torque because there’s no change in the position of the door even after applying the rotational force.

Note:
Torque is a vector quantity. It describes both magnitude and direction. Most of us think torque as scalar because the units of energy and torque are the same. But energy is a scalar, so we presume torque as scalar, but it is a vector quantity.