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Question

In the given figure below, a force of 120 N is applied horizontally on the upper block. Find the magnitude and direction of acceleration of the blocks A (aA) and B (aB).


A
aA=5 m/s2,right
aB=9 m/s2,right
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B
aA=9 m/s2,right
aB=5 m/s2,right
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C
aA=9 m/s2,right aB=1.5 m/s2,right
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D
aA=1.5 m/s2,right aB=9 m/s2,right
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Solution

The correct option is C aA=9 m/s2,right aB=1.5 m/s2,right
The FBDs of the blocks are as shown


We have from the FBDs as
N1=mAg=10g=100 N
N2=N1+20g=100+200=300 N
In the above situation, we see that the maximum possible value of friction between the blocks is fmax=μsN1=0.3×100=30 N

Considering that there is no slipping between the blocks, the acceleration of system will be
a=12020+10=4 m/s2

( only friction force between block A and block B is responsible for producing acceleration in block B)

f=mBa=20×4=80 N
f>(fs)max, it means our assumption is wrong and we can conclude that the blocks do not move together.

Now drawing the FBD of each block including horizonatal forces only, we have



aA=120fmaxmA=1203010=9 m/s2 towards right
and, aB=fmaxmB=3020=1.5 m/s2 towards right.

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