Question

The maximum value of mass of block C so that neither A nor B moves is (Given that mass of A is $100$kg and that of B is $140$kg. 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. $210$kg
• B. $190$kg
• C. $185$kg
• D. $162$kg

Answer 1

The correct option is D $162$kg

$\mu =0.3$

$M_A=100kg$

$M_B=140kg$

From the F.B.D of the blocks:

$T^{\prime \prime }=M_{c}g$

$T^{\prime }=2T$

$T^{\prime \prime }=\mu M_{A}g$

$fg=\mu [M_A+M_B]g$

$f_{AB}=\mu M_{A}g$

$T^{\prime \prime }=\mu M_{A}g+2\mu M_{A}g+\mu [M_A+M_B]g$

$=\mu g[4M_A+M_B]$

$M_{C}g=0.3g[4\times 100+140]$

$M_C=0.3\left[540\right]$

$=3\times 54$

$=162kg$