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 ${m_2}$. What acceleration (in $m{s^{ - 2}}$) would the same force provide if both the masses are tied together?
A. 4
B. 5
C. 6
D. 7

Answer 1

Newton’s second law of motion states that force is directly proportional to the acceleration produced, $F = m \times a$. Find the mass ${m_1}$ by dividing the Force $5N$ with its given acceleration and the mass ${m_2}$by dividing the Force $5N$ with its given acceleration. Add the two masses and find the acceleration produced by the resultant mass where the force will be the same $5N$.

Complete step by step answer:
We are given that 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 ${m_2}$.
We have to calculate the acceleration produced when the masses are tied together and with the same force provided.
Force is defined as the product of mass and acceleration.
$F = m \times a$
Here, the force applied is the same on masses ${m_1}$ and ${m_2}$
Mass will be obtained by dividing the force with the acceleration produced by the mass.
$m = \dfrac{F}{a}$
Mass ${m_1}$ is obtained by dividing the force of $5N$ with the acceleration of $8m{s^{ - 2}}$
${m_1} = \dfrac{F}{{{a_1}}} \\\ {a_1} = 8m{s^{ - 2}},F = 5N \\\ {m_1} = \dfrac{5}{8}kg \\\$
Mass ${m_2}$ is obtained by dividing the force of $5N$ with the acceleration of $24m{s^{ - 2}}$
${m_2} = \dfrac{F}{{{a_2}}} \\\ {a_2} = 24m{s^{ - 2}},F = 5N \\\ {m_2} = \dfrac{5}{{24}}kg \\\$
The resultant mass when both the masses are tied together will be
$M = {m_1} + {m_2} \\\ {m_1} = \dfrac{5}{8}kg,{m_2} = \dfrac{5}{{24}}kg \\\ \implies M = \dfrac{5}{8} + \dfrac{5}{{24}} \\\ M = \dfrac{{20}}{{24}} = \dfrac{5}{6}kg \\\$
The mass resulting when the two masses are combined is $\dfrac{5}{6}$kg.
Acceleration (in $m{s^{ - 2}}$) when both the masses are tied together is
$a = \dfrac{F}{m} \\\ F = 5N,m = \dfrac{5}{6}kg \\\ a = \dfrac{5}{{\dfrac{5}{6}}} \\\ \therefore a = 6m{s^{ - 2}} \\\$
The acceleration produced when the masses are tied together with the same force will be $6m{s^{ - 2}}$

So, the correct answer is “Option C”.

Note:
Acceleration is the rate of change of velocity per unit time. Acceleration increases when the velocity increases drastically and decreases with the velocity. Acceleration occurs when the speed of an object changes or when the direction of the object changes. Acceleration is a vector quantity.