Question

In the figure shown below, if the downward acceleration $a$ of $B$ is along the fixed incline, then find the accleration of $A$ if $A$ and $B$ remains in contact.

• A. $a\sin \alpha$
• B. $a\cot \alpha$
• C. $a\tan \theta$
• D. $a[\cos \alpha +\sin \alpha \cot \theta ]$

Answer 1

The correct option is D $a[\cos \alpha +\sin \alpha \cot \theta ]$

The component of acceleration of the block A and B are as shown in the figure below.
For the body B, components of acceleration are,
$a_x=a\cos \alpha$ and $a_y=a\sin \alpha$
From the constraint equation along normal to surface A,
$a_x\sin \theta +a_y\cos \theta =a_A\sin \theta$
From the above equations,
$a_A=\frac{a\cos \alpha \sin \theta }{\sin \theta }+\frac{a\sin \alpha \cos \theta }{\sin \theta }$
$a_A=a[\cos \alpha +\sin \alpha \cot \theta ]$