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 Cg4 The 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−4gsin30∘=4g−2g ∴a=4g−2g8=g4