Question

A block $A$ of mass $4\, kg$ is placed on another block $B$ of mass $5\, kg$, and the block $B$ rests on a smooth horizontal table. If the minimum force that can be applied on $A$ so that both the blocks move together is $12\, N$, the maximum force that can be applied on $B$ for the blocks to move together will be :

• A. 30 N
• B. 25 N
• C. 27 N
• D. 48 N

Answer 1

Answer: (C)

Here , $m_1=4\,kg,m_2=5\,kg$.
Force applied on $A , f = 12 \,N $,
This must at least be equal to force of kinetic friction applied on $A$ bt $B$
$f = f_k = μ_k R = μ_km_1\,g$
$12=f_k = μ_k \times 4\,g$
$∴ μ_k = 124 \,g = 3\,g$
As block $B$ is on smooth surface , therefore to move $A$ and $B$ togrther , (maximum) force $F$ required to be applied on $B =$ frictional force applied on a by A
$F = \frac{3}{g}(4+5)\,g=27\,N$