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  4. The coefficient of static friction, μ s, between block A of mass 2 kg and the table as shown in the figure, is 0.2. What would be the maximum mass value of block B so that the two blocks do not move ? The string and the pulley are assumed to be smooth and massless (g=10 m/s2)

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Q. The coefficient of static friction, $ {{\mu }_{s}}, $ between block $A$ of mass $2 \,kg$ and the table as shown in the figure, is $0.2$. What would be the maximum mass value of block $B$ so that the two blocks do not move ? The string and the pulley are assumed to be smooth and massless $ (g=10\,m/{{s}^{2}}) $Physics Question Image

ManipalManipal 2007Laws of Motion

Solution:

image
Free body diagram of two masses is
image
We get equations
$T+m a=f_{\mu}$
or $T=\mu N_{A}($ for $a=0)$
and $T=m a+m g$
or $T=m_{B} g$ (for $a=0$ )
$\therefore \mu N_{A}=m_{B} g $
$\Rightarrow m_{B}=\mu m_{A}$
$=0.2 \times 2=0.4\, kg $