A light string passing over a smooth light fixed pulley connects...

A light string passing over a smooth light fixed pulley connects two blocks of masses ${m}_{1}$ and ${m}_{2}$ . If the acceleration of the system is $\dfrac{g}{8}$ , then the ratio of masses is

Options

A $\dfrac{9}{7}$
B $\dfrac{8}{1}$
C $\dfrac{4}{3}$
D $\dfrac{5}{3}$

Correct answer

A. $\dfrac{9}{7}$

Step-by-step solution

Acceleration of the system can be written as, $a = \dfrac{\left({m}_{1} - {m}_{2}\right)g}{\left({m}_{1} + {m}_{2}\right)} = \dfrac{g}{8}$

$⇒ 8{m}_{1} - 8{m}_{2} = {m}_{1} + {m}_{2}$

$⇒ 7{m}_{1} = 9{m}_{2}$

$⇒ \dfrac{{m}_{1}}{{m}_{2}} = \dfrac{9}{7}$

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