Two masses M₁ and .M₂ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass M₂ is twice that of M₁. the acceleration of the system is a₁. When the mass M₂ is thrice that of M₁. The acceleration of The system is a₂. The ratio $\frac{a_{1}}{a_{2}}$ will be:

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$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{3}{2}$

answer is B.

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Detailed Solution

$\begin{array}{l} a = \frac{m_{2} g - m_{1} g}{m_{1} + m_{2}} \\ Case 1 M_{2} = 2 m_{1} \\ a_{1} = \frac{2 m_{1} g - m_{1} g}{3 m_{1}} \\ a_{1} = g / 3 \end{array}$

Case - 2

$\begin{array}{l} M_{2} = 3 m_{1} \\ a_{2} = \frac{3 m_{1} g - m_{1} g}{4 m_{1}} \\ a_{2} = \frac{g}{2} \\ \frac{a_{1}}{a_{2}} = \frac{\frac{g}{3}}{\frac{g}{2}} = \frac{2}{3} \end{array}$

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