Question 30 of 210

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 $2Mg$ force. In this situation, tension in the string is $\dfrac{x}{5}Mg$ 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: 6

Equation for $4M:2Mg-T=4Ma...\left(1\right)$
Equation for $M:T-Mg=Ma...\left(2\right)$
Adding both equation we get,
$Mg=5Ma\Rightarrow a=\dfrac{g}{5}$
Now, tension $T=Mg+Ma=\dfrac{6Mg}{5}$
Therefore, $x=6$