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)

$a=\frac{m_{2}g-m_{1}g}{m_1+m_2}$
Case $1M_2=2m_1$
$a_1=\frac{2m_{1}g-m_{1}g}{3m_1}$
$a_1=g/3$
Case $-2$
$M_2=3m_1$
$a_2=\frac{3m_{1}g-m_{1}g}{4m_1}$
$a_2=\frac{g}{2}$
$\frac{a_1}{a_2}=\frac{\frac{3}{g}}{\frac{g}{2}}=\frac{2}{3}$