A body constrained to move in the y-direction is subjected to a force `F=(2i+15j+16k)N`. The work done by this force in moving the body through a distance of 10 m along y-axis is

Options

A. 100 J
B. 150 J
C. 120 J
D. 200 J

Answer

To find the work done by the force on the body moving in the y-direction, we can use the formula for work done, which is given by the dot product of the force vector and the displacement vector.

### Step-by-Step Solution:

1. **Identify the Force Vector**:
The force vector is given as \( \mathbf{F} = 2\hat{i} + 15\hat{j} + 16\hat{k} \) N.

2. **Identify the Displacement Vector**:
Since the body is moving only in the y-direction through a distance of 10 m, the displacement vector can be represented as:
\[ \mathbf{d} = 0\hat{i} + 10\hat{j} + 0\hat{k} = 10\hat{j} \text{ m} \]

3. **Calculate the Dot Product**:
The work done \( W \) is calculated using the dot product of the force vector and the displacement vector:
\[ W = \mathbf{F} \cdot \mathbf{d} \]
\[ W = (2\hat{i} + 15\hat{j} + 16\hat{k}) \cdot (0\hat{i} + 10\hat{j} + 0\hat{k}) \]

4. **Perform the Dot Product Calculation**:
The dot product is calculated as follows:
\[ W = (2 \cdot 0) + (15 \cdot 10) + (16 \cdot 0) \]
\[ W = 0 + 150 + 0 \]
\[ W = 150 \text{ J} \]

5. **Conclusion**:
The work done by the force in moving the body through a distance of 10 m along the y-axis is \( 150 \text{ J} \).