Acceleration of Block on Smooth Inclined Plane
Category : JEE Main & Advanced
(1) When inclined plane is at rest
Normal reaction R = mg cos \[\theta \]
Force along a inclined plane
F = mg sin \[\theta \] ; ma = mg sin \[\theta \]
\[\therefore \] a = g sin \[\theta \]
(2) When a inclined plane given a horizontal acceleration 'b'
Since the body lies in an accelerating frame, an inertial force (mb) acts on it in the opposite direction.
Normal reaction R = mg cos \[\theta \] + mb sin \[\theta \]
and ma = mg sin \[\theta \] - mb cos \[\theta \]
\[\therefore \] a = g sin \[\theta \] - b cos \[\theta \]
Note :
\[\therefore \] b = g tan \[\theta \]
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