Two masses 2 kg and 3 kg are attached to

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Two masses $2 \,kg$ and $3 \,kg$ are attached to the end of the string passed over a pulley fixed at the top. The tension and acceleration are

A

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

B

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

C

$\frac{{21g}}{8};\,\frac{g}{5}$

D

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

Two masses $2 \,kg$ and $3 \,kg$ are attached to the end of the string passed over a pulley fixed at the top. The tension and acceleration are

$T = \frac{{2{m_1}{m_2}}}{{{m_1} + {m_2}}}g = \frac{{2 \times 2 \times 3}}{{2 + 3}}g = \frac{{12}}{5}g$

$a = \left( {\frac{{{m_2} - {m_1}}}{{{m_1} + {m_2}}}} \right)\;g $

$= \left( {\frac{{3 - 2}}{{3 + 2}}} \right)\;$

$g = \frac{g}{5}$