A body constrained to move in z direction is subjected to a force given by `vecF=(3hatj-10hatj+5hatk)N.` What is the work done by this force in moving the body through a distance of 5 m along z-axis?

Options

A. 15 J
B. `-15J`
C. `-50J`
D. `25J`

Answer

To solve the problem, we need to calculate the work done by the force when the body moves through a distance of 5 m along the z-axis.

### Step-by-step Solution:

1. **Identify the Force Vector**:
The force vector is given as:
\[ \vec{F} = 3\hat{i} - 10\hat{j} + 5\hat{k} \, \text{N} \]

2. **Identify the Displacement Vector**:
The displacement vector when the body moves 5 m along the z-axis is:
\[ \vec{d} = 0\hat{i} + 0\hat{j} + 5\hat{k} \, \text{m} \]

3. **Calculate the Work Done**:
The work done \( W \) by a force when moving through a displacement is given by the dot product of the force vector and the displacement vector:
\[ W = \vec{F} \cdot \vec{d} \]
Substituting the values:
\[ W = (3\hat{i} - 10\hat{j} + 5\hat{k}) \cdot (0\hat{i} + 0\hat{j} + 5\hat{k}) \]

4. **Perform the Dot Product**:
The dot product can be calculated as follows:
\[ W = (3 \cdot 0) + (-10 \cdot 0) + (5 \cdot 5) \]
This simplifies to:
\[ W = 0 + 0 + 25 = 25 \, \text{J} \]

5. **Conclusion**:
The work done by the force in moving the body through a distance of 5 m along the z-axis is:
\[ W = 25 \, \text{J} \]

### Final Answer:
The work done is **25 Joules**.