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 $1 M_2=2 m_1$
$ 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} $
$\frac{ a _1}{ a _2}=\frac{\frac{3}{ g }}{\frac{ g }{2}}=\frac{2}{3}$