Question

Two blocks $A$ and $B$ of masses $10\, kg$ and $15 \,kg$ 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 $0.2.\, A$ horizontal force of $200 \,N$ is applied to block $A$. The acceleration of the system is
(Take$\,g=10\,m \,s^{-2}$)

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

Answer 1

Answer: (B)

Here, Mass of block $A$, $m_{A}$ $=10 \,kg$
Mass of block $B$, $m_{B}$ $=15 \,kg$
Coefficient of friction between the blocks and the surface, $\mu$ $=0.2$
Applied force = $200\, N$
Force of friction on $A$ $=\mu N_{A}$ $=\mu m_{A} g$ $=0.2\times10\times10=20 \,N$
Force of friction on $B$ $=\mu N_{B}$ $=\mu m_{B} g$ $=0.2\times15\times10$ $=30\, N$
Taking two blocks forming one system, therefore net force acting on the blocks is
$F$ $=200-20-30=150\, N$
Let $a$ be common acceleration of the system.
$\therefore \quad$ $a=\frac{F}{m_{A} +m_{B}}$ $=\frac{150 N}{\left(10+15\right)kg}$ $=6 \,m$ $s^{-2}$