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By what acceleration, the wedge should move so that the block moves upwards along the surface of the wedge with an acceleration of $g\sin \theta $.
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A. $2g\cos \theta $
B. $g\sin \theta $
C. $2g\tan \theta $
D. $g\cos \theta $

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Last updated date: 17th Jul 2024
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Answer
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Hint:To construct a free-body diagram, we draw the point of concern, all forces acting on it, and resolve all force vectors into x– and y–components. A separate free-body diagram is required for each object in the question.

Complete step by step answer:
After drawing a free body diagram, we will get the following figure,
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In the following question, we observe with respect to wedge. Hence, we apply pseudo force on the block. After substituting the values from free body diagram we will get,
$ma\cos \theta - mg\sin \theta = ma' \\
\Rightarrow ma\cos \theta - mg\sin \theta = mg\sin \theta \\
\Rightarrow a\cos \theta = 2g\sin \theta \\
\Rightarrow a = \dfrac{{2g\sin \theta }}{{\cos \theta }} \\
\therefore a = 2g\tan \theta \\ $
Hence, the correct option is C.

Note:Four forces are not often applied to objects. In certain cases, the number of forces described by a free-body diagram may be one, two, or three. In a free-body diagram, the number of forces that must be drawn is not a hard and fast rule. There is only one guideline to drawing free-body diagrams: reflect all of the forces that exist with that object in the given situation.