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Question

Find the maximum value of the magnitude of force F for which the system will move together. Take g=10 m/s2.


A
20 N
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B
30 N
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C
50 N
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D
75 N
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Solution

The correct option is D 75 N
The FBDs of the blocks are as shown.
Given, the system of blocks will move together.
From the FBDs we have
N1=10g=100 N
N2=20g+N1=200+100=300 N
fmax=μsN1=0.5×100=50 N

Now, for the blocks to move together, friction force required to be acted on block B is
fmax=50 N
Hence, acceleration of the system is a=aB=fmaxmB=5020=2.5 m/s2
F=(mA+mB)a=30×2.5=75 N

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