Question

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

Answer 1

Answer: 5

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