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 small 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 $g\cot \theta$

The components of acceleration $a$ of the wedge and acceleration due to gravity $g$ is shown in the figure.

If the mass $m$ has to be fall freely, the component of acceleration of the wedge perpendicular to the incline should be equal to the component of acceleration due to gavity $g$perpendicular to the incline.
$\Rightarrow a\sin \theta =g\cos \theta$
Or, $a=g\cot \theta$