An object is kept on a smooth inclined plane


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An object kept on a smooth inclined plane of inclination theta with horizontal can be kept stationary relative to the incline by giving a horizontal acceleration to the inclined plane, equal to

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Mg sin θ = ma cosθ
cutting m from both sides gives us 

g sinθ= a cosθ
g sinθ/cosθ= a

as sinθ/cosθ = tanθ

so g tanθ= a

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