A) g
B) \[g\,\cot \,\theta \]
C) \[g\,\sin \theta \]
D) \[g\,\tan \,\theta \]
Correct Answer: B
Solution :
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].
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