Question

# Find the accelerations a1,a2 and a3 of the three blocks as shown in figure, if a horizontal force of 10 N is applied on the 3 kg block. The coefficient of static friction (μ) for all contact surfaces are shown in the figure. Take g=10 m/s2.

A
a1=a2=a3=56 m/s2
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B
a1=103 m/s2, a2=56 m/s2, a3=103 m/s2
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C
a1=103 m/s2, a2=103 m/s2, a3=56 m/s2
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D
a1=56 m/s2, a2=56 m/s2, a3=103 m/s2
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Solution

## The correct option is A a1=a2=a3=56 m/s2When force of 10 N is applied on 3 kg block, let us assume that all three blocks moves together with common acceleration a, then a=Fm=102+3+7=1012=56 m/s2 Friction between 2 kg block and 3 kg block: Required frictional force on 2 kg block f1=m1a=2×a=2×56=53 N Maximum frictional force on 2 kg block f1max=μ1N1=μ1m1g=0.2×2×10=4 N ∵(f1max>f1, hence block will move with that acceleration. Friction f2 between 3 kg and 7 kg block Required frictional force on 7 kg block f2=7a=7×56=356 N Maximum frictional force between 3 kg and 7 kg block f2max=μ2N2=μ2(m1+m2)g =0.3×(2+3)×10=15 N ∵(f2)max>f2, hence both blocks will move with that acceleration. Therefore, no sliping occurs anywhere, and all the 3 blocks will move with common acceleration of 56 m/s2 ⇒Option A is correct

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