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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, $g=9.8 \mathrm{~m} / \mathrm{s}^2$ )
Options:
When whole system is going upwards with acceleration $2 \mathrm{~m} / \mathrm{s}^2$, the value of $T_1$ is (use, $g=9.8 \mathrm{~m} / \mathrm{s}^2$ )
Solution:
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Verified Answer
The correct answer is:
$94.4 \mathrm{~N}$
$$
\text { The given situation is shown below }
$$
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 $5 \mathrm{~kg}$,
$$
\begin{aligned}
& & T_1-T_2-m_1 g & =m_1 a \\
\Rightarrow & & T_1-35.4-5 \times 9.8 & =5 \times 2 \\
\Rightarrow & & T_1-84.4 & =10^{\circ} \\
\Rightarrow & & T_1 & =10+84.4=94.4 \mathrm{~N}
\end{aligned}
$$
\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}
$$
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