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Question

# In the figure shown, find the acceleration (in m/s2) of the blocks if the wedge is fixed. (String is massless and inextensible)

A
2g
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B
g3
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C
g4
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D
g
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Solution

## The correct option is C g4The FBDs of the masses are as shown Let the direction of the acceleration a be as shown in the figure and tension in the string be T So, from the FBDs we have T−4g.sin30∘=4a⟹T−2g=4a........(i) And, 4g−T=4a.........(ii) From eq (i) & (ii) we have, 2g=8a⟹a=g4 Alternate: Let the two blocks collectively form a system. So, the acceleration of the system is given by a=Effective forceTotal mass Here, effective force on the system is given by 4g−4g sin 30∘=2g ∴a=4g−2g8=g4

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