Question

The acceleration of a body sliding down an inclined surface is:

• A. g sin θ
• B. g cos θ
• C. g tan θ
• D. none of these

Hint:

If the surface has friction, the acceleration decreases to $g(\sin \theta - \mu \cos \theta)$. However, in standard ideal cases where friction isn't mentioned, we consider only the gravity component.

Answer 1

The Correct Option is A

Step 1: Let the body of mass \( m \) slide a distance \( s \) down the smooth incline, starting from rest. The vertical height it drops through is \( h = s\sin\theta \).

Step 2: Since the incline is frictionless, mechanical energy is conserved: the loss in potential energy converts entirely into kinetic energy. \[ mgh = \frac{1}{2}mv^2 \implies v^2 = 2g\sin\theta \cdot s \]

Step 3: Compare this with the standard kinematic relation \( v^2 = 2as \) for motion starting from rest. Matching the two expressions for \( v^2 \) gives \( 2as = 2g\sin\theta \cdot s \), so the acceleration works out to: \[ \boxed{a = g\sin\theta} \]