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Q.

A force of $5 N$ produces an acceleration of $8 \frac{m}{S^{2}}$ in mass $m_{1} kg$ and acceleration of $24 \frac{m}{S^{2}}$ in mass $m_{2}$ kg. What would be the acceleration if the same force acts on both the masses combined together?

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a

4 \frac{m}{S^{2}}

b

5 \frac{m}{S^{2}}

c

6 \frac{m}{S^{2}}

d

7 \frac{m}{S^{2}}

answer is C.

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Detailed Solution

A force of

5 N

produces an acceleration of

8 \frac{m}{S^{2}}

in mass

m_{1}

kg and acceleration of

24 \frac{m}{S^{2}}

in mass

m_{2}

kg. If same forces act on both the masses combined together, the acceleration will be

6 m s^{- 2}

.
Given data in the problem,
Force,

F = 5 N

acceleration,

a_{1} = 8 \frac{m}{S^{2}}

acceleration,

a_{2} = 24 \frac{m}{S^{2}}

As we know that,

\Rightarrow F = m \times a

Force = mass \times acceleration

\Rightarrow m_{1} = \frac{F}{a_{1}} = \frac{5}{8}

\Rightarrow m_{2} = \frac{F}{a_{2}} = \frac{5}{24}

So, total mass

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

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

So, the acceleration produced in M

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

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

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

Acceleration will be

6 m s^{- 2}

.

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