Question

A force F = (3i + 2j -4k) N acts on a particle. The position of particle with respect to origin O is
r= (i +2j) m. Find the torque acting on the particle and calculate its magnitude.​

Answer 1

Answer:

torque= force perpendicular to r*(distance=r)

=>t= (3i+2j-4k)N*(i+2j)m

=>t=(3+4)Nm =7 Nm

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Answer 2

The torque acting on the particle and its magnitude is $8i-4j+4k$ and 9.79 N-m.

Explanation:

Given that,

Force, $F = (3i + 2j -4k)\ N$

The position of particle with respect to origin O is, $r= (i +2j)\ m$

We need to find the torque acting on the particle. We know that the torque acting on a particle is given by the dot product of force and position. We know that :

$\tau=F\times r\\\\\tau=(3i+2j-4k)\times (i+2j)\\\\\tau=\begin{pmatrix}8&-4&4\end{pmatrix}$

So, torque acting on the particle is $8i-4j+4k$. The magnitude of torque is :

$|\tau|=\sqrt{8^2+(-4)^2+(4)^2} \\\\\tau=9.79\ N-m$

So, the torque acting on the particle and its magnitude is $8i-4j+4k$ and 9.79 N-m. Hence, this is the required solution.

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