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 cont

Question

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

TestHub · Accepted Answer

When block does not slide with respect to the inclined plane,

$F_{1} =$ normal reaction $= m g \cos θ + m a \sin θ$

$∵ a = g \tan θ$

$∴ F_{1} = m g \cos θ + m (g \tan θ) \sin θ$

$= m g \sec θ = m g \sec 30 ° = \frac{2 m g}{\sqrt{3}}$

When incline plane is stationary,

$F_{2} = m g \cos θ = m g \cos 30 ° = \frac{\sqrt{3}}{2} mg$

$∴ \frac{F_{1}}{F_{2}} = \frac{4}{3}$

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