Question

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

• A. \(\frac{1}{3}\)
• B. \(\frac{2}{3}\)
• C. \(\frac{3}{2}\)
• D. \(\frac{1}{2}\)

Answer 1

The Correct Option is B

the acceleration ratio of two masses:

\(a_1 = \frac{M_2-M_1}{M_2+M_1} \times g \)

= \(\frac{2M_1-M_1}{3M_1} \times g\)

then, \(a_2 = \frac{3M_1-M_1}{4M_1} \times g = \frac{g}{2}\)

therefore, \(\frac{a_1}{a_2} = \frac{\frac{g}{3}}{\frac{g}{2}}\)

= \(\frac{2}{3}\)