• # question_answer A particle of mass m is resting on a wedge of angle $\theta$ as shown in the figure. The wedge is given an acceleration a. What is the value of a so that the mass m just falls freely? A)  g                    B) $g\,\cot \,\theta$C) $g\,\sin \theta$                       D) $g\,\tan \,\theta$

The acceleration a of the wedge should be such that in the time wedge moves distance BC, the particle must fall through a distance AB under gravity. Hence, $BC=\frac{1}{2}a{{t}^{2}}$and $AB=\frac{1}{2}g{{t}^{2}}.$ $\tan \theta =\frac{AB}{BC}=\frac{g}{a}or\,a=g\cot \theta$ Hence, the correction option is [b].