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=5m/s2,right aB=9m/s2,right
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B
aA=9m/s2,right aB=5m/s2,right
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C
aA=9m/s2,rightaB=1.5m/s2,right
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D
aA=1.5m/s2,rightaB=9m/s2,right
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Solution
The correct option is CaA=9m/s2,rightaB=1.5m/s2,right The FBDs of the blocks are as shown
We have from the FBDs as N1=mAg=10g=100N N2=N1+20g=100+200=300N
In the above situation, we see that the maximum possible value of friction between the blocks is fmax=μsN1=0.3×100=30N
Considering that there is no slipping between the blocks, the acceleration of system will be a=12020+10=4m/s2
(∵ only friction force between block A and block B is responsible for producing acceleration in block B)
⇒f=mBa=20×4=80N ∵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=120−fmaxmA=120−3010=9m/s2 towards right
and, aB=fmaxmB=3020=1.5m/s2 towards right.