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Physics-

General

Easy

Question

A body of mass $m$ is resting on a wedge of angle $theta$ as shown in figure. The wedge is given at acceleration $alpha$ . What is the value of a son that the mass $m$ just falls freely?

$g$
$g \sin θ$
$g \tan θ$
$g \cot θ$

The correct answer is: $g cot invisible function application theta$

The horizontal acceleration $a$ of the wedge should be such that in time the wedge moves the horizontal distance $B C$ . The body must fall through a vertical distance $A B$ under gravity. Hence,
$B C equals fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent$ and $A B equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent$
tan $theta equals fraction numerator A B over denominator B C end fraction equals fraction numerator g over denominator a end fraction$ or $a equals fraction numerator g over denominator t a n theta end fraction equals g blank c o t theta$

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