Question

A body moves a distance of 10 m under the action of force \(F = 10\) N. If the work done is 25 J, the angle which the force makes with the direction of motion is

• A. 0°
• B. 30°
• C. 60°
• D. None of these

Hint:

Work is maximum when force is along displacement (\(\theta = 0^\circ\)).

Answer 1

The Correct Option is D

To determine the angle between the force and the direction of motion, we use the work done equation:

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

where:

• \(W\) is the work done, given as 25 J.
• \(F\) is the force applied, 10 N.
• \(d\) is the distance moved, 10 m.
• \(\theta\) is the angle between the force and the direction of motion.

Plug the values into the formula:

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

Simplifying the equation:

\(25 = 100 \cdot \cos(\theta)\)

Solving for \(\cos(\theta)\):

\(\cos(\theta) = \frac{25}{100} = 0.25\)

The angle whose cosine is 0.25 is calculated using inverse cosine:

\(\theta = \cos^{-1}(0.25)\)

Calculating this angle, we get:

\(\theta \approx 75.52^\circ\)

Since 75.52° does not correspond to any of the provided options (0°, 30°, 60°), the correct answer is:

None of these