Question bank/JEE Main/Physics

Two men of masses m and m/2 starts climbing up on two massless
strings fixed at the ceiling with acceleration g and g/2 respectively.
The ratio of tensions in the two strings are 2x: y then find the value
of x + y.

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FBD of man of mass (m)
$T_{1} = 2mg$
FBD of man of mass (m/2)
$T_{2} = \frac{mg}{2}\left\lbrack \frac{3}{2} \right\rbrack = \frac{3mg}{4}$
$\Rightarrow T_{1}:T_{2}::8:3$

Source: Grass-G / P-06 Physics paper 14 October.docx