A force of 5 N produces an acceleration of 8 ms-2 on mass m1 and an acceleration of 24 ms-2 on mass m2. What is the acceleration, if both the masses are tied together?

A force of

5 N

produces an acceleration of

8 m s^{- 2}

on mass

m_{1}

and an acceleration of

24 m s^{- 2}

on mass

m_{2}

. The acceleration is

6 m s^{- 2}

if both the masses are tied together.
Given,
Force of the first mass,

F_{1} = 5 N

acceleration of first mass,

a_{1} = 8 m s^{- 2}

Force of second mass,

F_{2} = 5 N

acceleration of first mass,

a_{2} = 24 m s^{- 2}

According to Newton’s second law of motion,

F = ma

where

F

is the force applied/exerted,

m

is the mass and

a

is the acceleration of the body.
For the first mass, on substituting the given values, we get

\Rightarrow 5 = m_{1} \times 8

where

m_{1}

is the mass of the first mass.

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

Similarly, for the first mass, on substituting the given values, we get

\Rightarrow 5 = m_{2} \times 24

where

m_{2}

is the mass of the second mass.

{\Rightarrow m}_{2} = \frac{5}{24} kg

The total mass

(m)

if the bodies are tied together is

\Rightarrow m = {m_{1} + m}_{2}

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

\Rightarrow m = \frac{15 + 5}{24}

\Rightarrow m = \frac{20}{24}

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

Now, the acceleration

(a)

produced by the same force

(F)

provided if both the masses are tied together is

\Rightarrow a = \frac{F}{(m_{1} + m_{2})}

\Rightarrow a = \frac{5}{(5 / 6)}

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

Hence, the acceleration is

6 m s^{- 2}

A force of $5 N$ produces an acceleration of $8 m s^{- 2}$ on mass $m_{1}$ and an acceleration of $24 m s^{- 2}$ on mass $m_{2}$ . What is the acceleration, if both the masses are tied together?