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Two weights $w_1$ and $w_2$ are suspended to the two strings on a frictionless pulley. When the pulley is pulled up with an acceleration $g$, then the tension in the string is :
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Verified Answer
The correct answer is:
$\frac{4 w_1 w_2}{w_1+w_2}$
Equation of motion for first weight
$\begin{aligned} T-m_1 g & =m_1(g+a) \\ \Rightarrow \quad T-2 m_1 g & =m_1 a\ldots(1)\end{aligned}$
For second weight
$\begin{aligned} m_2 g-T & =m_2(a-g) \\ 2 m_2 g-T & =m_2 a\ldots(2)\end{aligned}$
On solving Eqs. (1) and (2)
$\begin{aligned} T & =\frac{4 m_1 m_2 g}{\left(m_1+m_2\right)} \\ & =\frac{4 w_1 w_2}{\left(w_1+w_2\right)}\end{aligned}$
$\begin{aligned} T-m_1 g & =m_1(g+a) \\ \Rightarrow \quad T-2 m_1 g & =m_1 a\ldots(1)\end{aligned}$
For second weight
$\begin{aligned} m_2 g-T & =m_2(a-g) \\ 2 m_2 g-T & =m_2 a\ldots(2)\end{aligned}$
On solving Eqs. (1) and (2)
$\begin{aligned} T & =\frac{4 m_1 m_2 g}{\left(m_1+m_2\right)} \\ & =\frac{4 w_1 w_2}{\left(w_1+w_2\right)}\end{aligned}$
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