Question

Moment of force F = 3i - 3j acting at R (0, 1, 1) about A (0, 1, 0) is

• A. -i-3j
• B. 3i+3j
• C. 3j
• D. none of these

Answer 1

Answer: (B)

3i+3j

Answer 2

To find the moment of a force $\vec{F}$ about a point $A$, we use the formula $\vec{M} = \vec{r} \times \vec{F}$, where $\vec{r}$ is the position vector from $A$ to the point of application of the force $R$.

Given:

• Force, $\vec{F} = 3\hat{i} - 3\hat{j}$
• Point $R(0,1,1)$
• Reference point $A(0,1,0)$

Step 1: Find the position vector $\vec{r}$ from $A$ to $R$: $\vec{r} = \vec{R} - \vec{A} = (0-0, 1-1, 1-0) = (0, 0, 1)$

Step 2: Compute the moment $\vec{M}$ of force about point $A$ using the cross product: $\vec{M} = \vec{r} \times \vec{F}$ $\vec{M} = (0, 0, 1) \times (3, -3, 0)$

Using the cross product formula: $\vec{M} = (0 \cdot 0 - 1 \cdot (-3), 1 \cdot 3 - 0 \cdot 0, 0 \cdot (-3) - 0 \cdot 3) = (3, 3, 0)$

Thus, the moment is: $\vec{M} = 3\hat{i} + 3\hat{j}$