Question

A body of mass 2 kg is acted upon by two forces, each of magnitude 1 N and inclined at \( 60^\circ \) with each other. The acceleration of the body in \( \text{m/s}^2 \) is 
\(\textit{(cos 60° = 0.5)}\)

• A. \( \sqrt{0.35} \)
• B. \( \sqrt{0.65} \)
• C. \( \sqrt{0.75} \)
• D. \( \sqrt{0.20} \)

Hint:

When forces are at an angle, resolve them into components and use the resultant force to calculate acceleration.

Answer 1

The Correct Option is C

Step 1: Resolve the forces.
The two forces act at an angle \( \theta = 60^\circ \). The resultant force \( F \) is given by: \[ F = \sqrt{(F_1^2 + F_2^2 + 2F_1F_2 \cos \theta)} \] Substitute the values: \[ F = \sqrt{(1^2 + 1^2 + 2 \times 1 \times 1 \times \cos 60^\circ)} = \sqrt{(1 + 1 + 1)} = \sqrt{3} \]
Step 2: Calculate the acceleration.
Using Newton's second law, the acceleration \( a \) is: \[ a = \frac{F}{m} = \frac{\sqrt{3}}{2} \approx \sqrt{0.75} \]
Step 3: Conclusion.
Thus, the correct answer is (C) \( \sqrt{0.75} \).