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

Answer: (B)

$\frac{2}{3}$

Answer 2

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, $\frac{a_1}{a_2} = \frac{\frac{g}{3}}{\frac{g}{2}}$

= $\frac{2}{3}$