Question

In the situation as shown in the figure if acceleration of $B$ is a, then find the acceleration of $A$ ($B$ always remains horizontal )

• A. $a\sin \theta$
• B. $a\cos \theta$
• C. $2a\tan \theta$
• D. $2a\cos \theta$

Answer 1

Answer: (D)

$2a\cos \theta$

Components of accelerations of $A$ and $B$ along normal $\left(\hat{n}\right)$ to the incline of wedge should be the same.
$\Rightarrow A\sin \theta =a\cos (2\theta -{90}^o)$
$\Rightarrow A\sin \theta \sin 2\theta$
$\Rightarrow A=2a\cos \theta$