Two masses 2 kg and 3 kg are attached to the end of the string passing over a pulley fixed at the top. The ratio of tension and acceleration is

1 : 6

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1 : 12

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12 : 1

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24 : 5

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Solution

The correct option is C 12 : 1
Tension in the siting $T = \frac{2 m_{1} m_{2}}{m_{1} + m_{2}} g$
$= \frac{2 \times 2 \times 3}{2 + 3} g = \frac{12}{5} g$
Acceleration of the system
$a = (\frac{2 m_{1} m_{2}}{m_{1} + m_{2}}) g$
$= (\frac{3 - 2}{3 + 2}) g = \frac{g}{5}$
$∴ \frac{T}{a} = \frac{12}{5} g \div \frac{g}{5} = \frac{12}{1}$

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