JEE Main 2019 — Rotational Motion Question with Solution

To determine the moment of the forces about point O, we need to calculate the moments of each force and then combine them vectorially.

First, consider force $$\overrightarrow{F_1}$$. This force acts along the z-axis at the point $$(2\overrightarrow{i}+3\overrightarrow{j})$$.

The position vector of the point of application of $$\overrightarrow{F_1}$$ relative to the origin O is:

Since $$\overrightarrow{F_1}$$ acts along the z-axis, we can express it as:

The moment of force $$\overrightarrow{F_1}$$ about point O is given by the cross product:

Substitute the values:

Compute the cross product:

So, the moment due to force $$\overrightarrow{F_1}$$ is: