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If $a_{1} and a_{2}$ are the acceleration in the first and second cases, the ratio $a_{1} : a_{2}$ is

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12 : 1

3 : 5

5 : 1

1 : 1

answer is C.

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Detailed Solution

$a_{1} = \frac{5 mg - mg}{m} = \frac{4 mg}{m}$

= 4g

$a_{2} = \frac{4 mg - 2 mg}{6 m}$

$= \frac{2 mg}{6 m} = \frac{g}{3}$

$\frac{a_{1}}{a_{2}} = \frac{4 g}{g / 3} = \frac{12}{1}$

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