Question

A constant force acts on two different masses independently producing accelerations $a_1$ and $a_2$. When the same force acts on their combined mass, the acceleration produced is

• A. $a_1 +a_2 $
• B. $a_1a_2 $
• C. $\frac{a_1a_2}{a_1 +a_2}$
• D. $\sqrt{a_1^2 +a_2^2}$

Answer 1

Answer: (C)

Here, $F = m_{1}a_{1} or , m_{1} = \frac{F}{a_{1}} $
$ F = m_{2}a_{2} or, m_{2} = \frac{F}{a_{2}} $
$ F = \left(m_{1 } +m_{2}\right)a$
$ or, a =\frac{F}{\left(m_{1}+m_{2}\right)} $
$ or, a = \frac{F}{\left(F / a_{1}\right)+\left(F / a_{2}\right)} = \frac{a_{1}a_{2}}{a_{1} +a_{2}}$