All surfaces shown in figure are smooth. System is released from rest. x and y components of acceleration of COM are

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${(a_{cm})}_{x} = \frac{m_{1} m_{2} g}{m_{1} + m_{2}}$

${(a_{cm})}_{y} = {(\frac{m_{2}}{m_{1} + m_{2}})}^{2} g$

${(a_{cm})}_{x} = \frac{m_{1} m_{2} g}{{(m_{1} + m_{2})}^{2}}$

${(a_{cm})}_{y} = (\frac{m_{2}}{m_{1} + m_{2}}) g$

answer is B, C.

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Detailed Solution

$a = \frac{Net pulling force}{Total mass} = \frac{m_{2} g}{m_{1} + m_{2}}$

$N o w, {(a_{cm})}_{x} = \frac{m_{1} a}{m_{1} + m_{2}} = \frac{m_{1} m_{2} g}{{(m_{1} + m_{2})}^{2}} {(a_{cm})}_{y} = \frac{m_{2} a}{m_{1} + m_{2}} = {(\frac{m_{2}}{m_{1} + m_{2}})}^{2} g$

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