Question

The situation shown in the figure, all strings and pulleys are ideal. If tension in the string connecting blocks $A$ and $C$ is $\frac{1350}{11 n} N$. The value of $n$ is___.

Answer 1

Equation of motion for block $C$ is
$m_{c} g-T=m_{c} a_{c}$
Or $180-T=18 a_{c}$ ...(i)
$T-45=9 a_{A}$ ...(ii)
and $2 T-45=9 a_{B}=9\left(\frac{a_{C}-a_{A}}{2}\right)$ ...(iii)
or $4 T-90=9 a_{C}-9 a_{A}$
or $4 T-90=9\left(\frac{180-T}{18}\right)-9\left(\frac{T-45}{9}\right)$
or $4 T+\frac{T}{2}+T=90+45=135$
$\therefore T=\frac{135}{5.5}=\frac{1350}{55}=\frac{1350}{11 n}$
Comparing with the given value, we have $n=5$