A block is kept on a smooth inclined plane of the angle of inclination 30 ° that moves with a constant acceleration so that the block does not slide relative to the inclined plane. Let F 1 be the contact force between the block and the plane. Now the inclined plane stops and let F 2 be the contact force between the two in this case. Then F 1 F 2 is

Step-by-step solution

When block does not slide with respect to the inclined plane, F 1 = normal reaction = m g cos ⁡ θ + m a sin ⁡ θ ∵ a = g tan ⁡ θ ∴ F 1 = m g cos ⁡ θ + m g tan ⁡ θ sin ⁡ θ = m g sec ⁡ θ = m g sec ⁡ 30 ° = 2 m g 3 When incline plane is stationary, F 2 = m g cos ⁡ θ = m g cos ⁡ 30 ° = 3 2 mg ∴ F 1 F 2 = 4 3