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

In this scenario, the acceleration \( a \) of the block on the inclined plane is given by the equation: \[ a = g \sin \theta \] We are told that the acceleration is half of the acceleration due to gravity, so: \[ \frac{g}{2} = g \sin \theta \] Solving for \( \theta \): \[ \sin \theta = \frac{1}{2} \] \[ \theta = 30^\circ \] Thus, the angle of inclination \( \theta \) is \( 30^\circ \) for the block to have half the acceleration due to gravity.