Question

If a force of $ 10 \, \text{N} $ displaces a body by $ 5 \, \text{m} $ in the direction of the force, the work done is:

• A. \( 2 \, \text{J} \)
• B. \( 50 \, \text{J} \)
• C. \( 0 \, \text{J} \)
• D. \( 5 \, \text{J} \)

Hint:

Key Fact: Work \( = Fd\cos\theta \); maximum when \( \theta = 0^\circ \)

Answer 1

The Correct Option is B

The problem requires us to calculate the work done when a force of \(10 \, \text{N}\) displaces a body by \(5 \, \text{m}\). Work done (\(W\)) is calculated using the formula:

\(W = F \times d \times \cos(\theta)\)

Where:

• \(F\) is the force applied;
• \(d\) is the displacement;
• \(\theta\) is the angle between the force and displacement.

In this scenario, the force and displacement are in the same direction, meaning \(\theta = 0^\circ\). Therefore, \(\cos(0^\circ) = 1\), simplifying our calculation:

\(W = 10 \, \text{N} \times 5 \, \text{m} \times 1\)

\(W = 50 \, \text{J}\)

Thus, the work done is \(50 \, \text{J}\).

Answer 2

The work done on an object when a force is applied can be calculated using the formula:

Work Done (W) = Force (F) × Displacement (d) × cos(θ)

In this problem, the force is applied in the direction of displacement, so the angle θ = 0° and cos(0°) = 1. 

Thus, the formula simplifies to:

W = F × d

Given:

• Force (F) = 10 N
• Displacement (d) = 5 m

Substitute the given values into the formula:
W = 10 N × 5 m = 50 J

Therefore, the work done is: 50 J