Question

A force of 26 N is acting on a body of mass 2 kg in the x-y plane. The force is directed at an angle \(\cos^{-1}\left(\frac{12}{13}\right)\) with the x-axis. The component of acceleration along y-axis is

• A. \(8 \, \text{m s}^{-2}\)
• B. \(3 \, \text{m s}^{-2}\)
• C. \(5 \, \text{m s}^{-2}\)
• D. \(12 \, \text{m s}^{-2}\)

Hint:

Always find sine using \(\sin\theta = \sqrt{1-\cos^2\theta}\) when cosine is given.

Answer 1

The Correct Option is C

Step 1: Resolving the force.
Given \[ \cos\theta = \frac{12}{13} \Rightarrow \sin\theta = \frac{5}{13} \]
Step 2: Calculating y-component of force.
\[ F_y = F \sin\theta = 26 \times \frac{5}{13} = 10 \, \text{N} \]
Step 3: Using Newton’s second law.
\[ a_y = \frac{F_y}{m} = \frac{10}{2} = 5 \, \text{m s}^{-2} \]
Step 4: Conclusion.
The acceleration along y-axis is \(5 \, \text{m s}^{-2}\).