A block of mass m sits on an incline of angle θ with no friction. What is its acceleration down the plane?

• A. a = g cos θ
• B. a = g sin θ
• C. a = g tan θ
• D. a = g

Answer: (B)

When an object slides on a frictionless incline, gravity can be split into two components: one perpendicular to the plane and one parallel to it. The perpendicular component, m g cos θ, is balanced by the normal force, so it doesn’t cause motion. The parallel component, m g sin θ, is what pulls the block down the slope. With no friction, this parallel component is the net force along the plane, so the acceleration is a = F/m = (m g sin θ)/m = g sin θ. This makes sense because the acceleration depends on how steep the incline is: zero at θ = 0 and approaching g as θ → 90°.

The other expressions don’t fit: g cos θ is the force component perpendicular to the plane, not along it; g tan θ isn’t a direct gravity component along the plane; and g is the total gravitational acceleration, but only the parallel component drives the motion on the incline.