A block $A$ of mass $M$ rests on a horizontal table. A light string connected to it passes over a fr

Question

A block $A$ of mass $M$ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block $B$ of mass $2M$ is suspended. The coefficient of kinetic friction between the block and the table is $\mu_k$. When the block $A$ is sliding on the table,  the tension in the string is

Professor PC Thomas Classes · Answer

Equations: $2Mg - T = 2Ma$ and $T - \mu_k Mg = Ma$. Add them: $2Mg - \mu_k Mg = 3Ma \implies a = \frac{(2-\mu_k)g}{3}$. Put $a$ in second eq: $T = \mu_k Mg + M\left[\frac{(2-\mu_k)g}{3}\right] = \frac{3\mu_k Mg + 2Mg - \mu_k Mg}{3} = \frac{2Mg + 2\mu_k Mg}{3} = \frac{2Mg(1+\mu_k)}{3}$.