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Question

In the arrangement shown in figure , if the acceleration of B is $$\vec{a}$$ , then find the acceleration of A

A
In the $$ a \tan \theta $$
B
$$ a \sin \alpha $$
C
$$a \cot \theta $$
D
$$a ( \sin \alpha \cot \theta + \cos \alpha )$$
Solution
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Correct option is B. $$a \cot \theta $$
Along the normal both $$A$$ and $$B$$ have same acceleration.
B will are along the Inclined path
$$a_{A} \cos(90^o - \theta) = a_{B} cos \theta $$
$$a_{A} \sin \theta = a_{B} cos \theta$$
$$a_{A} = \dfrac{a}{sin \theta }(cos \theta) $$
$$ = a \cot \theta$$

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