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A force of $5 N$ produces an acceleration of $8 m / s^{2}$ on a mass $m_{1}$ and an acceleration of $24 m / s^{2}$ on a mass $m_{2}$ .

What acceleration would the same force provide if both the masses were tied together?

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8 m / s^{2}

9 m / s^{2}

6 m / s^{2}

4 m / s^{2}

answer is C.

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Detailed Solution

If both the masses are tied together, the same force will provide an acceleration of

6 m / s^{2}

.
According to Newton’s second law of motion,
We know,

F = m a

= 5 N

Since

F = ma

Then

\Rightarrow m_{1} = F / a_{1}

\Rightarrow m_{2} = F / a_{2}

if both the masses are tied together, then total mass

M = m_{1} + m_{2}

\Rightarrow M = \frac{F}{a_{1}} + \frac{F}{a_{2}}

\Rightarrow M = \frac{5}{8} + \frac{5}{24}

\Rightarrow M = \frac{5}{6} kg

Hence acceleration produced by the tied masses, i.e. total masses

\Rightarrow a = \frac{F}{M}

\Rightarrow a = \frac{5}{\frac{5}{6}}

\Rightarrow a = 6 m / s^{2}

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