A force produces an acceleration of a₁ in a body and the same force produces an acceleration of a₂ in another body. If the two bodies are combined and the same force is applied on the combination, the acceleration produced in it is

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$a_{1} + a_{2}$

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

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

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

answer is C.

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Detailed Solution

Given that

$F = m_{1} a_{1} and F = m_{2} a_{2}$

$F = (m_{1} + m_{2}) a$

$F = (\frac{F}{a_{1}} + \frac{F}{a_{2}}) a$

$\Rightarrow a = \frac{a_{1} a_{2}}{a_{1} + a_{2}}$

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