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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 g4
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
T4g.sin30=4aT2g=4a........(i)
And, 4gT=4a.........(ii)
From eq (i) & (ii) we have,
2g=8aa=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
4g4g sin 30=4g2g
a=4g2g8=g4

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