Question

A block slides down a smooth inclined plane and its acceleration is found to be half the acceleration due to gravity. What is the angle of inclination \( \theta \) of the plane?

• A. \( 45^\circ \)
• B. \( 60^\circ \)
• C. \( 30^\circ \)
• D. \( 90^\circ \)

Hint:

In problems involving inclined planes, the acceleration is proportional to the sine of the angle of inclination.

Answer 1

The Correct Option is C

The acceleration \( a \) of the block on the inclined plane is \( a = g \sin \theta \). Given that \( a = \frac{g}{2} \), we have \( \frac{g}{2} = g \sin \theta \). This simplifies to \( \sin \theta = \frac{1}{2} \), yielding \( \theta = 30^\circ \). Therefore, the angle of inclination is \( 30^\circ \) when the block's acceleration is half that of gravity.