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Question

# Find the acceleration of the two blocks A and B respectively, assuming them to be at rest initially. Take g=10 m/s2.

A
4 m/s2,2 m/s2
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B
2 m/s2,4 m/s2
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C
2 m/s2,2 m/s2
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D
4 m/s2, zero
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Solution

## The correct option is C 2 m/s2,2 m/s2The FBDs of the blocks are as shown Given, the force acting on the block A is F=180 N We have from the FBDs N1=20g=200 N f1 max=μ1N1=(0.8)(20g)=0.8×200=160 N N2=N1+10g=200+100=300 N f2 max=μ2N2=(0.4)(300)=120 N Since, F>f1 max and f1 max>f2 max, both the blocks will accelerate. Now, let us assume both the blocks will move together, then Common acceleration is given by ac=180−f2 maxmA+mB=180−12030=2 m/s2 Again for block B: f1−f2 max=mBac⇒ f1=10×2+120=140 N Since, f1<f1 max, our assumption is right Hence, the friction will be static in nature & the two blocks will move together with common acceleration of 2 m/s2

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