Motion On An Inclined Plane

Following NCERT Class 11, Chapter 5 (Laws of Motion), when an object rests on a frictionless inclined plane, the only force producing motion along the surface is the component of gravity directed down the slope, equal to mg sinθ. Resolving the weight into components, the component along the incline is mg sinθ and the component perpendicular to it is mg cosθ, which is balanced by the normal reaction. Applying Newton's Second Law along the incline, ma = mg sinθ, so the acceleration is a = g sinθ, independent of mass. Substituting, a = 10 × sin30° = 10 × 0.5 = 5 m/s². Option 10 m/s² wrongly uses free fall, ignoring the incline. Option 8.66 m/s² uses cos30° instead of sin30°, resolving along the wrong axis. Option 2.5 m/s² halves the correct value without justification. A key conceptual point is that the normal reaction here is mg cosθ, which is smaller than the full weight, yet it plays no role in the acceleration along the slope; only the parallel gravity component matters for frictionless motion. This separation of perpendicular and parallel components is the heart of inclined-plane analysis. Plausibility check: the acceleration must be less than g for any incline below vertical, and 5 m/s² is exactly half of g at 30°, which is consistent and dimensionally correct in m/s².