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A hanging mass M is connected to a four times bigger mass by using a string pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is $\frac{x}{5} Mg$ for x=_________. Neglect mass of the string and friction of the block (bigger mass) with ice slab.
(Given g = acceleration due to gravity)

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answer is 6.

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Detailed Solution

$Using {\vec{F}}_{net} = m \vec{a}$
$\begin{matrix} 2 Mg - T = 4 Ma \\ \frac{T - Mg = Ma}{\Rightarrow a = \frac{g}{5}} \end{matrix}$
$T = Mg + Ma = Mg + \frac{Mg}{5} = \frac{6}{5} Mg$

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