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Net Force

A force produ...

Question

A force produces an acceleration of $a_{1}$ in a body and the same force produces an acceleration of $a_{2}$ in another body. If the two bodies are combined and the same force is applied on the combination, then the acceleration produced in it is

A

a_{1} + a_{2}

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B

\frac{a_{1} + a_{2}}{a_{1} a_{2}}

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C

\frac{a_{1} a_{2}}{a_{1} + a_{2}}

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D

\sqrt{a_{1} a_{2}}

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Solution

The correct option is D $\frac{a_{1} a_{2}}{a_{1} + a_{2}}$
Here, suppose two body has masses $m_{1}$ and $m_{2}$ .
According to the question,
$F = m_{1} a_{1}$ and $F = m_{2} a_{2}$ .
Now, if the two bodies are combined and the same force is applied on the combination, then:
$F = m a$
or $F = (m_{1} + m_{2}) a$
or $F = (m_{1} + m_{2}) a$
or $F = (\frac{F}{a_{1}} + \frac{F}{a_{2}}) a$
So, $a = \frac{a_{1} a_{2}}{a_{1} + a_{2}}$

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