JEE Main & Advanced Physics NLM, Friction, Circular Motion Acceleration of Block on Smooth Inclined Plane

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 :

The condition for the body to be at rest relative to the inclined plane : a = g sin \[\theta \] - b cos \[\theta \] = 0

\[\therefore \] b = g tan \[\theta \]