Question

A force F=(2i+3j-2k)N acts on a particle whose coordinates are (1m, 2m, 3m) find the torque acting on the particle​

Answer 1

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Answer 2

Answer:

Torque acting on the particle is (13i - 8j + k) Nm.

Given:

[Note that bold letters represent vectors.]

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

Coordinates of the point = (1 m, 2 m, 3 m)

where m is the unit of distance, i.e., meters.

Find:

The torque acting on the particle.

Solution:

Torque is given by,

Torque = Force × Distance

τ = F × r

where r is the position vector of the particle.

Here, coordinates of the particle are (1, 2, 3).

Position vector of the particle, r = 1i + 2j + 3k

∴ Torque, τ = F × r

                  = (2i + 3j - 2k) × (1i + 2j + 3k)

                   = $\left[\begin{array}{ccc}\hat i&\hat j&\hat k\\2&3&-2\\1&2&3\end{array}\right]$

                   = i[9 + 4] - j[6 + 2] + k[4 - 3]

                  = 13i - 8j + k

$Torque, \ \tau = 13 \hat i - 8 \hat j + \hat k$

Hence, torque acting on the particle is τ  = (13i - 8j + k) Nm.

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