Question

If ${\mu }_s$ and ${\mu }_k$ represent the coefficient of static and kinetic friction respectively with appropriate suffixes for the two bodies shown, find the acceleration of the system $[$ Take $g=10{\text{m/s}}^2]$

• A. $10{\text{m/s}}^2$
• B. $20{\text{m/s}}^2$
• C. $15.5{\text{m/s}}^2$
• D. Zero

Answer 1

The correct option is D Zero

FBD of the blocks,

The maximum (limiting) frictional force on this $5\text{kg}$ block
$f_{ma{x}_1}={\mu }_{s_1}{N}_1=0.6\times 50=30\text{N}$



The maximum frictional force on this $2\text{kg}$ block
$f_{{max}_2}={\mu }_{s_2}{N}_2=0.5\times 2\times 10=10\text{N}$
Total frictional force on this $5\text{kg}$ and $2\text{kg}$ block will be $=40\text{N}$
FBD of $3\text{kg}$ block

The maximum force due to $3\text{kg}$ block is $T_2=30\text{N}$

Since the applied force $T_2<f_{{max}_1}+f_{{max}_2}$, system will remain stationary.