Question

A block slides down a smooth inclined plane, and its acceleration is found to be \( \frac{g}{8} \). If \( g \) is the acceleration due to gravity, what is the angle of inclination \( \theta \) of the plane?

• A. \( \tan^{-1} \left( \frac{1}{8} \right) \)
• B. \( \tan^{-1} \left( \frac{1}{2} \right) \)
• C. \( \tan^{-1} \left( \frac{1}{4} \right) \)
• D. \( \tan^{-1} \left( \frac{1}{16} \right) \)

Hint:

For inclined plane problems involving acceleration, use the formula \( a = g \sin \theta \) to find the angle of inclination when acceleration is known.