Two masses M_{1} and M_{2} are tied together | vedclass

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(B) The acceleration of a system of two masses $M_{1}$ and $M_{2}$ connected by a string over a frictionless pulley is given by the formula:$a = \frac

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$\frac{2}{3}$

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(B) The acceleration of a system of two masses $M_{1}$ and $M_{2}$ connected by a string over a frictionless pulley is given by the formula:$a = \frac{|M_{2} - M_{1}|}{M_{1} + M_{2}} g$Case $1$: Given $M_{2} = 2M_{1}$.$a_{1} = \frac{|2M_{1} - M_{1}|}{M_{1} + 2M_{1}} g = \frac{M_{1}}{3M_{1}} g = \frac{g}{3}$Case $2$: Given $M_{2} = 3M_{1}$.$a_{2} = \frac{|3M_{1} - M_{1}|}{M_{1} + 3M_{1}} g = \frac{2M_{1}}{4M_{1}} g = \frac{g}{2}$Now,calculating the ratio $\frac{a_{1}}{a_{2}}$:$\frac{a_{1}}{a_{2}} = \frac{g/3}{g/2} = \frac{2}{3}$Therefore,the correct option is $B$.

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