A horizontal force $F$ produces an acceleration of $6 m / s^{2}$ on a block resting on a smooth horizontal surface. The same force produces an acceleration of $3 m / s^{2}$ on a second block resting on a smooth horizontal surface. If the two blocks are tied together and the same force acts, the acceleration produced will be:

9 m / s^{2}

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2 m / s^{2}

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4 m / s^{2}

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\frac{1}{2} m / s^{2}

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Solution

The correct option is B $2 m / s^{2}$
Here, $F = m_{1} a_{1}$ and $F = m_{2} a_{2}$ .
Now if we tie both of them together then $F = m a$ and $m = m_{1} + m_{2}$
$\frac{F}{a} = \frac{F}{a_{1}} + \frac{F}{a_{2}}$
If the same force acts, the acceleration produced will be, $a = \frac{(a_{1} a_{2})}{(a_{1} + a_{2})} = 2 m / s^{2}$ .

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The correct option is B 2 m/s2Here, F=m1a1 and F=m2a2. Now if we tie both of them together then F=ma and m=m1+m2Fa=Fa1+Fa2If the same force acts, the acceleration produced will be, a=(a1a2)(a1+a2)=2 m/s2.