NIMCET 2024 — Mathematics PYQ

1. Given Data

• Magnitude of Force vector ($|F|$) = $40\text{ N}$

• Magnitude of Displacement vector ($|D|$) = $3\text{ m}$

• Angle between force and displacement ($\theta$) = $60^{\circ }$

2. Formula

Work done ($W$) is a scalar quantity defined as the dot product (scalar product) of the force vector and the displacement vector:

$$W=\vec{F}\cdot \vec{D}$$

$$W=|F|\cdot |D|\cdot \cos (\theta )$$

Where:

• $|F|$ is the magnitude of the applied force.

• $|D|$ is the magnitude of the displacement.

• $\theta$ is the angle between the directional paths of force and displacement.

3. Step-by-Step Calculation

Substitute the given values into the algebraic formula:

$$W=40\times 3\times \cos (60^{\circ })$$

We know that the standard trigonometric value for $\cos (60^{\circ })$ is $\frac{1}{2}$:

$$W=40\times 3\times \frac{1}{2}$$

Simplify the calculation by multiplying the constants:

$$W=120\times \frac{1}{2}$$

$$W=60\text{ J}$$

4. Conclusion

The work done by the force in moving the object along the path from point $P$ to point $Q$ evaluates to exactly $60\text{ Joules}$.

Therefore, the correct option matches option (D).

Correct Answer: (D) $60\text{ J}$