A person of mass M is stationary w.r.t. a weighing scale at the top of the wedge as shown in the fig. The wedge is on a frictionless inclined plane which makes an angle $θ$ with the horizontal. The reading in the weighing scale is

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The wedge and person slide down the smooth incline with $a = g sin θ$ along the incline.

Vertical component of this acceleration is $a_{y} = g sin^{2} θ$ (downwards).

$M g - N = M a_{y} \Rightarrow N = M g (1 - sin^{2} θ) = M g cos^{2} θ$ .

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