Physics - NLM Question with Solution | TestHub

Let the constant force be $F$.

When the force acts on the first mass $m_1$, the acceleration is $A_1$.

$F=m_1{A}_1\Rightarrow m_1=\frac{F}{A_1}$

When the force acts on the second mass $m_2$, the acceleration is $A_2$.

$F=m_2{A}_2\Rightarrow m_2=\frac{F}{A_2}$

When the same force acts on the combined mass $M=m_1+m_2$, the acceleration is $A$.

$A=\frac{F}{m_1+m_2}$

Substituting the values of $m_1$ and $m_2$:

$A=\frac{F}{\frac{F}{A_1}+\frac{F}{A_2}}$

$A=\frac{F}{F\left(\frac{1}{A_1}+\frac{1}{A_2}\right)}$

$A=\frac{1}{\frac{A_1+A_2}{A_1{A}_2}}$

$A=\frac{A_1{A}_2}{A_1+A_2}$

Answer: $\frac{A_1{A}_2}{A_1+A_2}$