Two masses of $5 \mathrm{~kg}$ and $3 \mathrm{~kg}$ are suspended with the help of massless inextensible strings as shown in figure below.
When whole system is going upwards with acceleration $2 \mathrm{~m} / \mathrm{s}^2$, the value of $T_1$ is (use, $g=9.8 \mathrm{~m} / \mathrm{s}^2$ )

• A

  $35.4 \mathrm{~N}$
• B

  $23.6 \mathrm{~N}$
• C

  $59 \mathrm{~N}$
• Correct answer
  D

  $94.4 \mathrm{~N}$

Solution

$$ \text { The given situation is shown below } $$
Equation of motion for body $m_2$, $$ \begin{aligned} T_2-m_2 g & =m_2 a \\ T_2-3 g & =3 \times 2 \\ T_2 & =3 g+6=3 \times 9.8+6=35.4 \mathrm{~N} \end{aligned} $$ Equation of motion of mass of $5 \mathrm{~kg}$, $$ \begin{aligned} & & T_1-T_2-m_1 g & =m_1 a \\ \Rightarrow & & T_1-35.4-5 \times 9.8 & =5 \times 2 \\ \Rightarrow & & T_1-84.4 & =10^{\circ} \\ \Rightarrow & & T_1 & =10+84.4=94.4 \mathrm{~N} \end{aligned} $$

Hence, the correct answer is option: 'D'.