question_answer

Given in the figure are two blocks \[A\] and \[B\] of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force \[F\] as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block \[B\] is

A) 100 N  

B) 80 N

C) 120 N

D) 150 N

Correct Answer: C

Solution :

[c] F.B.D. of block A and block B for block A: If block A is at equilibrium, then \[{{f}_{1}}={{W}_{A}}=20N\] If friction is static, \[{{f}_{1}}\le {{\mu }_{1}}{{N}_{1}}\] Or \[20\le 0.1\times F\Rightarrow F\ge \frac{20}{0.1}=200N\] Hence, limiting value of friction between the blocks. \[{{f}_{1}}=0.1\times 200=20N\] From F.B.D, of block B: \[{{f}_{2}}={{f}_{1}}+{{W}_{b}}=20+100=120N\] Alternative method: If we take both blocks together as system, them For equilibrium of the system I vertical direction. \[{{f}_{2}}={{W}_{A}}+{{W}_{B}}=20+100=120N\]