Question

Two blocks $A$ and $B$ weighing $2\text{kg}$ and $8\text{kg}$ respectively are tied with an inextensible string. The coefficient of kinetic and static friction between the blocks and the horizontal surface is $0.25$ and $0.3$ respectively. If horizontal force $F=25\text{N}$, then find the acceleration of block $A$ and $B$.

• A. $2.5{\text{m/s}}^2$
• B. $2{\text{m/s}}^2$
• C. $\text{Zero}$
• D. $4{\text{m/s}}^2$

Answer 1

The correct option is C $\text{Zero}$

Given,
${\mu }_k=0.25$
${\mu }_s=0.3$
$F=25\text{N}$
Initially both the blocks are at rest,
Then, maximum static friction force, $F_s={\mu }_s(m_A+m_B)g=0.3(2+8)\times 10$
$=30\text{N}$
$\because F_s\le F_{s\left(max\right)}$
A and B blocks will not move
$\therefore$ Acceleration of block A and B =0