An object is kept on a smooth inclined plane of inclination 1 in l . Find the horizontal acceleration that should be imparted to the inclined plane such that the object remains stationary relative to

Question

An object is kept on a smooth inclined plane of inclination 1 in l . Find the horizontal acceleration that should be imparted to the inclined plane such that the object remains stationary relative to the inclined plane.

TestHub · Accepted Answer

The object moves a height of 1 m when it travels a distance $l$ along the incline.

$H e r e, \sin θ = \frac{1}{l}$

Let required acceleration of inclined plane be a for the object to remain stationary relative to incline, we have

$\sin θ = \frac{1}{l}$

$\tan θ = \frac{1}{\sqrt{l^{2} - 1}}$

$m a \cos θ = m g \sin θ$

$a = g \tan θ$ $= \frac{g}{\sqrt{l^{2} - 1}}$

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