Question

A body moves a distance of $10\, m$ along a straight line under a action of $5\, N$ force. If work done is $25 \,J$, then angle between the force and direction of motion of the body will be

• A. $75^{\circ}$
• B. $60^{\circ}$
• C. $45^{\circ}$
• D. $30^{\circ}$

Answer 1

The Correct Option is B

To solve this problem, we need to find the angle between the force applied to the body and the direction of its motion using the work-energy principle.

First, let's recall the work done by a force formula:

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

where:

• W is the work done.
• F is the magnitude of the force.
• d is the distance moved by the body.
• \theta is the angle between the force and the direction of motion.

We are given:

• W = 25 \, \text{J}
• F = 5 \, \text{N}
• d = 10 \, \text{m}

Now, let's substitute these values into the formula and solve for \theta:

25 = 5 \cdot 10 \cdot \cos(\theta)

This simplifies to:

25 = 50 \cdot \cos(\theta)

Divide both sides by 50 to isolate \cos(\theta):

\cos(\theta) = \frac{25}{50} = 0.5

The angle whose cosine is 0.5 is 60^\circ.

Therefore, the angle between the force and the direction of motion is 60^\circ.

The correct answer is:

60^{\circ}