A body moves from point A to point B under the action of a force varying in magnitude as shown in the force displacement graph. Find total work done by the force :

Options

A. 10 J
B. 50 J
C. 60 J
D. 40 J

Answer

To find the total work done by the force as a body moves from point A to point B, we can follow these steps:

### Step 1: Understand the Force-Displacement Graph
The force-displacement graph shows how the force varies with displacement. The work done by a force is equal to the area under the force-displacement curve.

### Step 2: Identify the Shape of the Area
From the description, we can see that the area under the curve consists of a triangle and a trapezium. We need to calculate the area of these shapes to find the total work done.

### Step 3: Calculate the Area of the Triangle
The triangle is formed from the origin (0,0) to the point (5,10).
- The base of the triangle is 5 units (from 0 to 5 on the x-axis).
- The height of the triangle is 10 units (from 0 to 10 on the y-axis).

The area \(A_{triangle}\) can be calculated using the formula for the area of a triangle:
\[ A_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 10 = 25 \text{ joules} \]

### Step 4: Calculate the Area of the Trapezium
The trapezium is formed between the points (5,10) and (7,5).
- The lengths of the parallel sides are 10 units (at x=5) and 5 units (at x=7).
- The height of the trapezium is the difference in x-coordinates, which is \(7 - 5 = 2\) units.

The area \(A_{trapezium}\) can be calculated using the formula for the area of a trapezium:
\[ A_{trapezium} = \frac{1}{2} \times (\text{length of side 1} + \text{length of side 2}) \times \text{height} = \frac{1}{2} \times (10 + 5) \times 2 = \frac{1}{2} \times 15 \times 2 = 15 \text{ joules} \]

### Step 5: Calculate Total Work Done
Now, we can find the total work done \(W\) by adding the areas of the triangle and the trapezium:
\[ W = A_{triangle} + A_{trapezium} = 25 + 15 = 40 \text{ joules} \]

### Conclusion
The total work done by the force as the body moves from point A to point B is **40 joules**.

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