Question

Two forces of magnitude 4 N act on an object of mass 1 kg: \( \vec{F}_1 \) at 30° to x-axis and \( \vec{F}_2 \) along y-axis. Find the magnitude of acceleration.

• A. \( 6.9\ \text{m/s}^2 \)
• B. \( 7.6\ \text{m/s}^2 \)
• C. \( 4.3\ \text{m/s}^2 \)
• D. \( 8.0\ \text{m/s}^2 \)

Hint:

Break forces into components and use Pythagoras’ theorem for resultant.

Answer 1

The Correct Option is A

Components of \( \vec{F}_1 \): \[ F_{1x} = 4\cos(30^\circ) = 4 \cdot \frac{\sqrt{3}}{2} = 2\sqrt{3},\ F_{1y} = 4\sin(30^\circ) = 2 \] Total y-force = \( F_{1y} + F_2 = 2 + 4 = 6 \), Resultant force: \[ F = \sqrt{(2\sqrt{3})^2 + 6^2} = \sqrt{12 + 36} = \sqrt{48} = 6.9\ \text{N} \] Acceleration \( a = \frac{F}{m} = \frac{6.9}{1} = 6.9\ \text{m/s}^2 \)