Two masses $2 k g$ and $3 k g$ are attached to the end of the string passed over a frictionless pulley fixed at the the top. The tension in the string and acceleration of the masses are

\frac{7 g}{8}, \frac{7 g}{8}

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\frac{21 g}{8}, \frac{g}{8}

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\frac{12 g}{8}, \frac{g}{5}

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\frac{12 g}{5}, \frac{g}{5}

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Solution

The correct option is D $\frac{12 g}{5}, \frac{g}{5}$
Both the masses will have same acceleration being attached to the same string. Using the below two formulas for 2 mass system,
$T = \frac{2 m_{1} m_{2}}{m_{1} + m_{2}} g = \frac{2 \times 2 \times 3}{2 + 3} g = \frac{12 g}{5}$
$a = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g = (\frac{3 - 2}{2 + 3}) g = \frac{g}{5}$

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