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Explain the Acceleration of Block on Smooth Inclined Plane.

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(1) When inclined plane is at rest. 

Normal reaction R = mg cos θ 

Force along a inclined plane F = mg sin θ 

ma = mg sin θ 

a = g sin θ

(2) When a inclined plane given a horizontal acceleration ‘b’. Since the body lies in an accelerating frame, an inertial acts on it in the opposite direction. 

Normal reaction R = mg cos θ + mb sin θ 

and ma = mg sin θ – mb cos θ 

a = g sin θ – b cos θ

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