question_answer

In figure, the coefficient of friction between the floor and the block B is The coefficient of friction between the blocks B and A is 0.2. The mass of A is m/2 and that 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) 0.15 mg  

B) 0.05 mg

C) 0.1 mg             

D) 0.45 mg

Correct Answer: D

Solution :

[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\[F-{{\mu }_{B}}({{m}_{B}}+{{m}_{A}})g=({{m}_{B}}+{{m}_{A}})a\] \[F=({{m}_{B}}+{{m}_{A}})g+{{\mu }_{B}}({{m}_{B}}+{{m}_{A}})g\] \[=\left( m+\frac{m}{2} \right)(0.2g)+(0.1)\left( m+\frac{m}{2} \right)g\] \[=\left( \frac{3}{2}m \right)(0.2g)+\left( \frac{3}{2}m \right)(0.1g)=\frac{0.9}{2}mg=0.45mg\]