question_answer

A block \[A\] weighing \[100\,\,kg\] rests on a block \[B\] and is tied with a horizontal string to the wall at\[C\]. Block \[B\] weighs\[200\,\,kg\]. The coefficient of friction between \[A\] and \[B\] is \[0.25\] and between \[B\] and the surface is\[\frac{1}{3}\]. The horizontal force \[P\] necessary to move the block \[B\] should be\[(g=10\,\,m/{{s}^{2}})\]

A) \[1150\,\,N\]                    

B) \[1250\,\,N\]

C) \[1300\,\,N\]                    

D)  \[1420\,\,N\]

Correct Answer: B

Solution :

Friction between block \[A\] and block \[B\] and between block \[B\] and surface will oppose the\[P\]. \[\therefore \]  \[P={{F}_{AB}}+{{F}_{BS}}\]                 \[={{\mu }_{AB}}{{m}_{A}}g+{{\mu }_{BS}}({{m}_{A}}+{{m}_{B}})g\]                 \[=0.25\times 100\times 10+\frac{1}{3}(100+200)\times 10\]                 \[=1250\,\,N\]