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-

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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