Two masses \(M _{1}\) and \(M _{2}\) are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass \(M _{2}\) is twice that of \(M_{1}\). the acceleration of the system is \(a_{1}\). When the mass \(M_{2}\) is thrice that of \(M_{1}\). The acceleration of The system is \(a_{2}\). The ratio \(\frac{a_{1}}{a_{2}}\) will be.

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Answer & Solution

Correct Answer

(B) \(\frac{2}{3}\)

Detailed explanation

\(a=\frac{m_{2} g-m_{1} g}{m_{1}+m_{2}}\)

\(Case 1\) \(M_{2}=2 m_{1}\)

\(a_{1}=\frac{2 m_{1} g-m_{1} g}{3 m_{1}}\)

\(a_{1}=g / 3\)

Case \(-2\)

\(M_{2}=3 m_{1}\)

\(a_{2}=\frac{3 m_{1} g-m_{1} g}{4 m_{1}}\)

\(a_{2}=\frac{g}{2}\)

\(\frac{a_{1}}{a_{2}}=\frac{\frac{g}{3}}{\frac{g}{2}}=\frac{2}{3}\)

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