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A force of $5 N$ produce an acceleration of $8 m / s²$ on a mass $m_{1}$ and an acceleration of $24 m / s²$ on a mass $m_{2}$ , the acceleration of masses if both are tied together is [[1]] $m / s²$ .

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Detailed Solution

The acceleration of the masses tied together is

6 m / s²

.
The force on mass

m_{1}

is equal to

5 N

and the acceleration on the mass is

8 m / s²

and therefore the mass

m_{1}

is equal to,
⇨

m = \frac{F}{a}

⇨

m_{1} = \frac{5}{8} kg

The mass

m_{2}

is equal to,
⇨

m_{2} = \frac{5}{24} kg

The mass

m_{2}

is equal to

\frac{5}{24}

kg.
When the two masses are tied then,
⇨

m_{1} + m_{2} = \frac{5}{8} + \frac{5}{24}

= \frac{5}{6} kg

The acceleration of the masses tied together is equal to,

a = \frac{F}{m_{1} + m_{2}}

⇨

= \frac{5}{\frac{5}{6}}

⇨

= \frac{30}{5}

⇨

= 6 m / s² {^{}}^{}

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