• question_answer DIRECTIONS (Qs 51): Read the following passage and answer the questions that follows A block of mass $15\text{ }kg$ is placed over a frictionless horizontal surface. Another block of mass $10\text{ }kg$ is placed over it, that is connected with a light string passing over two pulleys fastened to the $15\text{ }kg$ block. A force $F=80N$is applied horizontally to the free end of the string. Friction coefficient between two blocks is$0.6$. The portion of the string between $10kg$ block and the upper pulley is horizontal. Pulley string and connecting rods are massless. (Take $g=10\text{ }m/{{s}^{2}}$) The magnitude of acceleration of the $10\text{ }kg$ block is A)  $3.2\text{ }m/{{s}^{2}}$                  B)  $2.0\text{ }m/{{s}^{2}}$C)  $1.6\text{ }m/{{s}^{2}}$                  D)  $0.8\text{ }m/{{s}^{2}}$

First, let us check upto what value of F, both blocks move together. Till friction becomes limiting, they will be moving together. Using the FBDs $10\text{ }kg$ block will not slip over the $15\,kg$ block till acceleration of $15\,kg$ block becomes maximum as it is created only by friction force exerted by $10\,kg$ block on it. ${{a}_{1}}>{{a}_{2(\max )}}$ $\frac{F-f}{10}=\frac{f}{15}$ for limiting condition as f maximum is 60N. $F=100N$ Therefore, for $F=80\,N,$ both will move together. Their combined acceleration, by applying NLM using both as system, $F=25a$                 $a=\frac{80}{25}=3.2\,m/{{s}^{2}}$