Block $A$ weighing $100$ kg rests on a block $B$ and is tied with a horizontal string to the wall at $C$. Block $B$ weighs $200 \,kg$. The coefficient of friction between $A$ and $B$ is $0.25$ and between $B$ and the surface is $1/3$. The horizontal force $P$ necessary to move the block $B$ should be ........ $N$ $(g = 10\,m/{s^2})$
AIIMS 2017, Difficult
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(b) Friction between block $A$ and block $B$ & between block $B$ and surface will oppose the $P$
$\therefore $ $P = {F_{AB}} + {F_{BS}}$ $ = {\mu _{AB}}{m_A}g + {\mu _{BS}}({m_A} + {m_B})g$
$ = 0.25 \times 100 \times 10 + \frac{1}{3}(100 + 200) \times 10$ $=1250\, N$
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