Question

Two blocks $A$ and $B$ of masses $6\text{kg}$ and $3\text{kg}$ rest on a smooth horizontal surface as shown in the figure. If coefficient of friction between $A$ and $B$ is $0.4$, find the maximum horizontal force which can make them move without separation. (Take $g=10m/s^2$)

• A. $72\text{N}$
• B. $40\text{N}$
• C. $36\text{N}$
• D. $20\text{N}$

Answer 1

The correct option is C $36\text{N}$


Maximum frictional force on block $B$ is
$f=uN=u{m}_{B}g$
$=0.4\times 3\times 10=12\text{N}$

Hence maximum acceleration of the block $B$ is
$a=\frac{f}{m_B}=\frac{12}{3}=4{\text{m/s}}^2$
If both the blocks move without separation then, acceleration of both the blocks should be same.
Therefore,
$F_{max}=(m_A+m_B)a$
$F_{max}=(6+3)\times 4$
$F_{max}=36\text{N}$