Question

All pulleys are light and smooth, strings are light and inextensible
Consider the case when $M\to \infty$ (See fig)

• A. acceleration of $m$ is $g$ upward
• B. Net force on $m$ is $mg/3$ upward
• C. Tension in the string connecting $M$ is $\frac{4mg}{9}$
• D. Tension in the string connecting $m$ is $2mg$

Answer 1

The correct option is A acceleration of $m$ is $g$ upward

$M_g-T=M_a\to \left(1\right)T-mg=ma\to \left(2\right)\left(1\right)+\left(2\right)\Rightarrow (M-m)g=(M+m)a\therefore a=\left(\frac{M-m}{M+m}\right)g=\left(\frac{1-\frac{m}{M}}{1-\frac{m}{M}}\right)g\therefore asM\to \infty ,a=g(\because \frac{m}{M}\to 0)$