Question

A small block of mass $m$ rests on a smooth wedge of angle $\theta$. With what horizontal acceleration $a$ should the wedge be pulled, as shown in the figure, so that the block falls freely.

• A. $g\cos \theta$
• B. $g\sin \theta$
• C. $g\cot \theta$
• D. $g\tan \theta$

Answer 1

The correct option is C $g\cot \theta$


By using constrained equation, component of acceleration of the wedge and the block perpendicular to the incline should be equal
$a\sin \theta =g\cos \theta$
$a=g\cot \theta$