Two masses ' m 1 ' and ' m 2 ' ( m 1 m 2 ) tied to a massless, inextensible string are hanging over a light frictionless pulley as shown. When the system is free to move,

Question

Two masses ' m 1 ​ ' and ' m 2 ​ ' ( m 1 ​ > m 2 ​ ) tied to a massless, inextensible string are hanging over a light frictionless pulley as shown. When the system is free to move, the acceleration of the masses is g /4 . The masses ' m 1 ​ ' and ' m 2 ​ ' are related as [ g = acceleration due to gravity]

TestHub · Accepted Answer

For an Atwood machine, the acceleration $a$ of the masses is given by:

$a = \frac{∣ m _{1} - m _{2} ∣}{m _{1} + m _{2}} g$

Given that the acceleration $a = \frac{g}{4}$ , we can write:

$\frac{∣ m _{1} - m _{2} ∣}{m _{1} + m _{2}} g = \frac{g}{4}$

Canceling $g$ from both sides and cross-multiplying:

$4∣ m_{1} - m_{2} ∣ = m_{1} + m_{2}$

Since $m_{1} > m_{2}$ :

$4 (m_{1} - m_{2}) = m_{1} + m_{2}$

$4 m_{1} - 4 m_{2} = m_{1} + m_{2}$

$3 m_{1} = 5 m_{2}$

Answer: $3 m_{1} = 5 m_{2}$

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