Question

The maximum value of mass of block $C$ so that neither $A$ nor $B$ moves is (Given that mass of $A$ is $100kg$ and that of $B$ is $140kg$. Pulleys are smooth and friction coefficient between $A$ and $B$ and between $B$ and horizontal surface is :($\mu =0.3,g=10m/s^2$).

• A. $210kg$
• B. $190kg$
• C. $185kg$
• D. $162kg$

Answer 1

The correct option is D $162kg$


$\mu =0.3$
$M_A=100kg$
$M_B=140kg$
From the F.B. D of the blocks:
$T"=M_{c}g$
$T^{\prime }=2T$
$T=\mu M_{A}g$
$T"=\mu M_{A}g+2\mu M_{A}g+\mu [M_A+M_B]g$
$=\mu g[4M_A+M_B]$
$M_{c}g=0.3g[4\times 100+140]$
$M_c=0.3\left[540\right]$
$=3\times 54$
$=162kg$