Physics - NLM Question with Solution | TestHub

For an Atwood machine with masses $m_1$ and $m_2$ ($m_2>m_1$), the acceleration $a$ is given by:

$a=\frac{m_2-m_1}{m_2+m_1}g$

Given that $a=\frac{g}{n}$, we can write:

$\frac{m_2-m_1}{m_2+m_1}g=\frac{g}{n}$

$\frac{m_2-m_1}{m_2+m_1}=\frac{1}{n}$

Dividing the numerator and denominator of the left side by $m_1$:

$\frac{\frac{m_2}{m_1}-1}{\frac{m_2}{m_1}+1}=\frac{1}{n}$

Cross-multiplying yields:

$n\left(\frac{m_2}{m_1}-1\right)=\frac{m_2}{m_1}+1$

$n\frac{m_2}{m_1}-n=\frac{m_2}{m_1}+1$

$\frac{m_2}{m_1}(n-1)=n+1$

$\frac{m_2}{m_1}=\frac{n+1}{n-1}$

Answer: $\frac{n+1}{n-1}$