Question

Two blocks $A$ and $B$ of masses $10kg$ and $15kg$ are placed in contact with each other rest on a rough horizontal surface as shown in the figure. The coefficient of friction between the blocks and surface is $\mathrm{0.2.}A$ horizontal force of $200N$ is applied to block $A$. The acceleration of the system is
(Take$g=10m{s}^{-2}$)

• A. $4m$ $s^{-2}$
• B. $6m$ $s^{-2}$
• C. $8m$ $s^{-2}$
• D. $10m$ $s^{-2}$

Answer 1

Answer: (B)

Here, Mass of block $A$, $m_A$ $=10kg$
Mass of block $B$, $m_B$ $=15kg$
Coefficient of friction between the blocks and the surface, $\mu$ $=0.2$
Applied force = $200N$
Force of friction on $A$ $=\mu N_A$ $=\mu m_{A}g$ $=0.2\times 10\times 10=20N$
Force of friction on $B$ $=\mu N_B$ $=\mu m_{B}g$ $=0.2\times 15\times 10$ $=30N$
Taking two blocks forming one system, therefore net force acting on the blocks is
$F$ $=200-20-30=150N$
Let $a$ be common acceleration of the system.
$\therefore$ $a=\frac{F}{m_A+m_B}$ $=\frac{150N}{\left(10+15\right)kg}$ $=6m$ $s^{-2}$