Question

A force of $5N$ produces an acceleration of $8m{s^ - }^2$ on a mass ${m_1}$ and an acceleration of $24m{s^ - }^2$ on a mass of ${m_2}$. What acceleration would the same force provide if both the masses are tied together?
A. $12m{s^ - }^2$
B. $6m{s^ - }^2$
C. $10m{s^ - }^2$
D. $18m{s^ - }^2$

Answer 1

The relationship between force and acceleration is described by Newton’s second law of motion.
The force is directly proportional to the acceleration
When we increase the force the acceleration is also increased.

Complete step by step answer:
The force acting on the object is directly proportional to the acceleration of the body with the mass being the constant of proportionality
The equation $F = ma,$
$m$ is the mass
$a$ is the acceleration
It is based on Newton’s first law of motion, the object stays at the rest position until the force acts on it also it is in constant velocity and direction until force acts on it.
the given force is,
$F = 5N$
The given acceleration is,
$a = 8$
We know that the formula is,
$F = ma$
Now substitute the values in the above equation and find the mass,
$5 = {m_1} \times 8$
By solving the above equation,
${m_1} = \dfrac{5}{8}kg$
Now we have to find the second mass,
$F = {m_2} \times 24$
By solving the equation ${m_2}$ is,
${m_2} = \dfrac{5}{{24}}kg$
In this question, both masses are tied together,
Total mass $m = {m_1} + {m_2}$
$m = \dfrac{5}{8} + \dfrac{5}{{24}}$
After solving the above equation the total mass will be,
$m = \dfrac{{20}}{{24}}kg$
Now the force is,
$F = ma$
$5 = \left( {\dfrac{{20}}{{24}}} \right)a$
Now solving the equation the acceleration will be $6m{s^ - }^2$.

So, the correct answer is “Option B”.

Note:
When the velocity gets increased over some time we said that the body gets accelerates
The object gets accelerates when the force acting on it
Generally, the mass resists the acceleration.