A wedge has a weight of 9kg . And a block has a weight of 2kg If the block starts sliding with an angle of 45° with the horizontal then what is accelaration of the wedge?


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Question Number 102753 by Dwaipayan Shikari last updated on 11/Jul/20

$A w e d g e h a s a w e i g h t o f 9 k g . A n d a b l o c k h a s a w e i g h t o f 2 k g$ $I f t h e b l o c k s t a r t s s l i d i n g w i t h a n a n g l e o f 45 ° w i t h t h e$ $h o r i z o n t a l t h e n w h a t i s a c c e l a r a t i o n o f t h e w e d g e ?$
	Answered by mr W last updated on 11/Jul/20

	$N = m g \cos θ - m a \sin θ$ $M a = N \sin θ$ $M a = (m g \cos θ - m a \sin θ) \sin θ$ $(M + m \sin^{2} θ) a = m g \sin θ \cos θ$ $\Rightarrow a = \frac{m g \sin θ \cos θ}{M + m \sin^{2} θ}$ $= \frac{2 g \times \frac{1}{2}}{9 + 2 \times \frac{1}{2}} = \frac{g}{10}$
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