A light string passing over a smooth light pulley connects two blocks of masses $a$ and $b$ (vertically). If the acceleration of the system is $\frac{g}{8}$ , then the ratio of the masses (i.e., $\frac{b}{a}$ ) is:

9 : 7

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1 : 2

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1 : 1

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5 : 3

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Solution

The correct option is A $9 : 7$

Let mass of two blocks be $a$ and $b$ respectively and their common acceleration be $a c c$ .
Applying equation of motion, assuming b>a
$b g - T = b \times a c c$
$T - a g = a \times a c c$
Substituting value of $a c c$ as $g / 8$ and eliminating $T$ ,
we get $b : a = 9 : 7$

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A light string passing over a smooth light pulley connects two blocks of masses a and b(vertically). If the acceleration of the system is g8, then the ratio of the masses (i.e., ba) is:

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