Question

A block is kept on a smooth inclined plane of angle of inclination 30° that moves with a constant acceleration so that the block does not slide relative to the inclined plane. Let F₁ be the contact force between the block and the plane. Now the inclined plane stops and let F₂ be the contact force between the two in this case. Then F₁/F₂ is –

• A. 1
• B. 4/3
• C. 2
• D. 3/2

Answer 1

Answer: (B)

4/3

Answer 2

From Lami’s theorem

$\frac{mg}{\sin(90{^\circ} + \theta)} = \frac{N_{1}}{\sin 90{^\circ}} = \frac{ma}{\sin(\pi –\theta)}$ $N_{1} = \frac{mg}{\cos\theta}$

When incline plane is at rest

^$\frac{N_{1}}{N_{2}} = \frac{1}{\cos^{2}\theta} = \frac{1}{\cos^{2}30{^\circ}} = 4/3$