question_answer 51)

                  In Fig. the co-efficient of friction between the floor and the body B is 0.1. The coefficient of friction between the bodies B and A is 0.2. A force F is applied as shown on B. The mass of A is m/2 and of B is m. Which of the following statements are true?                 (a) The bodies will move together if \[F=0.25\,mg\].                 (b) The body A will slip with respect to B if F = \[F=0.5\,mg\].                 (c) The bodies will move together if \[F=0.5\,mg\]                 (d) The bodies will be at rest if \[F=0.1\,mg\]                 (e) The maximum value of F for which the two bodies will move together is \[0.45\,\,\,mg\].

Answer:

                  (a, b, d, e) Force of friction between the floor and body B,                 \[{{f}_{1}}\,=\mu \,\left( m+\frac{m}{2} \right)\,g=\,0.1\,\times \,1.5\,\,mg\,=\,0.15\,\,mg\]                 Force of friction between bodies A and B,                 \[{{f}_{2}}=0.2\,\,\times \,\frac{m}{2}\,\,g=0.1\,\,mg\]                 Two bodies will move together if \[F={{f}_{1}}+{{f}_{2}}=0.25\text{ }mg\]