Physics - NLM Question with Solution | TestHub

Total mass of the system, $M=m_1+m_2+m_3=2+3+5=10\text{ kg}$

Acceleration of the system, $a=\frac{F}{M}=\frac{30}{10}=3{\text{ m/s}}^2$

Let $T_1$ be the tension in the string connecting $m_1$ and $m_2$.
Equation of motion for $m_1$:
$T_1=m_{1}a=2\times 3=6\text{ N}$

Let $T_2$ be the tension in the string connecting $m_2$ and $m_3$.
Equation of motion for the system of $m_1$ and $m_2$:
$T_2=(m_1+m_2)a=(2+3)\times 3=15\text{ N}$

Therefore, the tensions in the connecting strings are $6\text{ N}$ and $15\text{ N}$.

Answer: $15$ N; $6$ N