Question

The coefficient of static friction between the two blocks shown in the figure is ‘$\mu$’ and the table is smooth. The maximum value of ‘F’ so that both blocks moves together, is

• A. $\mu (M+m)g$
• B. $\mu mg$
• C. $\mu Mg$
• D. $\frac{\mu m(M+m)g}{M}$

Answer 1

The correct option is D $\frac{\mu m(M+m)g}{M}$


Let both the blocks are moving together with same acceleration a, then
$a=\frac{F}{M+m},f=Ma=\frac{MF}{M+m}$
For no relative motion to be there between the blocks, $f\le f_L$
i.e., $\frac{MF}{M+m}\le \mu mg\Rightarrow F\le \frac{\mu m(M+m)g}{M}$