Find the accelerations of the blocks A and B for the figure shown, if the system is initially at rest. Take g=10m/s2.
A
43m/s2, zero
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B
zero, 53m/s2
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C
3m/s2,3m/s2
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D
3m/s2, zero
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Solution
The correct option is D3m/s2, zero The FBDs of the blocks are as shown.
Given, force applied on the block A is F=50N
We have from the FBDs of the blocks N1=10g=100N f1max=0.2×100=20N N2=N1+20g=100+200=300N f2max=(0.4)(300)=120N
Since, f2 max>f1 max, block B will be at rest. ⇒ acceleration of the block B will be zero.
For block A: Since, F>f1 max, it will accelerate and the friction will be kinetic in nature ∴ Kinetic friction acting on block A is fk=μN1=0.2×10g=20N
So, acceleration of the block A is given by, aA=F−fkmA=50−2010=3m/s2