First slide

Two block problem

Question

A 4 kg block A is placed at the top of 8 kg block B which rests on a smooth table. A just slips on B when a force of 20 N is applied on A. The maximum horizontal force F required to make both A & B move together is

Moderate

A

36 N
B

5 N
C

40 N
D

60 N

Solution

$\large F_{max}=\mu _s.mg{(1+\frac {M}{m})}$ where M = Mass of the block on which force F is applied. and m = Mass of the upper block.
$\large 20=\mu _s\times4\times10\times{(1+\frac {4}{8})}\Rightarrow\mu_s =1/3$
$\large \therefore F_{max}=\frac 13\times4\times10\times{(1+\frac {8}{4})}N\Rightarrow N=40N$

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