Minimum work will be done if the angle between the impressed force and displacement caused is

Options

A. `90^(@)`
B. `60^(@)`
C. `45^(@)`
D. zero

Explanation

To solve the problem of determining the angle at which the minimum work is done when a force is applied to an object, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Work Done Formula**:
The work done (W) by a force (F) when it moves an object through a displacement (S) is given by the formula:
\[ W = F \cdot S = F S \cos \theta \]
where \(\theta\) is the angle between the force and the displacement.

2. **Identify the Condition for Minimum Work**:
To minimize the work done, we need to minimize the value of \(\cos \theta\). The cosine function varies between -1 and 1. The minimum value of \(\cos \theta\) is 0.

3. **Determine the Angle Corresponding to Minimum Work**:
The cosine of an angle is zero at:
\[ \theta = 90^\circ \]
This means that when the angle between the force and the displacement is 90 degrees, the work done is minimized.

4. **Conclusion**:
Therefore, the minimum work will be done when the angle between the impressed force and the displacement is:
\[ \theta = 90^\circ \]

### Final Answer:
The minimum work will be done if the angle between the impressed force and displacement is **90 degrees**.