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Question

Find the acceleration of the two bodies (A and B), if the system shown is initially at rest.
Take g=10 m/s2.

A
aA=aB=43 m/s2
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B
aA=43 m/s2;aB=0
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C
aA=0;aB=43 m/s2
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D
aA=2 m/s2;aB=4 m/s2
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Solution

The correct option is A aA=aB=43 m/s2
The FBDs of the blocks are as shown


N1=10g=100 N
N2=N1+5g=100+50=150 N
fmax=μN1=0.5×100=50 N

Assuming that the two blocks move together, then the Common acceleration is
ac=Fm1+m2=2015=43 m/s2

From FBD of B: Required frictional force f to make them move together is
f=mac=5×43=203 N
Since, 203 N<50 N
f<fmax, it means our assumption was right, they will move together
Hence, aA=aB=43 m/s2

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