Question

In figure, the coefficient of friction between the floor and the block B is $0.1$. The coefficient of friction between the blocks B and A is $0.2$. The mass of A is $m/2$ and of B is m. What is the maximum horizontal force F can be applied to the block B so that two blocks move together?

• A. $0.15mg$
• B. $0.05mg$
• C. $0.1mg$
• D. $0.45mg$

Answer 1

Answer: (D)

Here, $m_{A}=\frac{m}{2}, m_{B}=m$
$\mu_{A}=0.2, \mu_{B}=0.1$
Let both the blocks are moving with common acceleration a.Then,
$a=\frac{\mu_{A}m_{A}g}{m_{A}}=\mu_{A}g=0.2g$
and $F - \mu_{B}\left(m_{B} + m_{A}\right)g = \left(m_{B} + m_{A}\right)a$
$F=\left(m_{B}+m_{A}\right)a+\mu_{B} \left(m_{B}+m_{A}\right)g$
$=\left(m+\frac{m}{2}\right)\left(0.2 g\right)+\left(0.1\right) \left(m+\frac{m}{2}\right)g$
$=\left(\frac{3}{2}m\right)\left(0.2g\right)+\left(\frac{3}{2}m\right)\left(0.1g\right)=\frac{0.9}{2}mg=0.45\,mg$