If a force of $ 2 ext{ N}$ gives a mass $ m_1 $ an acceleration of $ 8 ext{ m s}^{-2}$ and a mass $ m_2 $

Question

If a force of $ 2 	ext{ N}$ gives a mass $ m_1 $ an acceleration of $ 8 	ext{ m s}^{-2}$ and a mass $ m_2 $ an acceleration of $ 15 	ext{ m s}^{-2}$, what will be the total mass if both the masses were tied together?

Examoogle · Accepted Answer

The correct answer is Option D: $\frac{23}{60} 	ext{ kg}$. To find the total mass, we first determine the individual masses using Newton's second law, $F = m 	imes a$. By calculating $m_1 = \frac{F}{a_1}$ and $m_2 = \frac{F}{a_2}$, we find $m_1 = \frac{2}{8} = 0.25 	ext{ kg}$ and $m_2 = \frac{2}{15} \approx 0.133 	ext{ kg}$. The total mass when combined is $m_{total} = m_1 + m_2 = \frac{1}{4} + \frac{2}{15} = \frac{15 + 8}{60} = \frac{23}{60} 	ext{ kg}$.

Step-by-Step Solution & Concepts:
To find the total mass, we first determine the individual masses using Newton's second law, $F = m 	imes a$. By calculating $m_1 = \frac{F}{a_1}$ and $m_2 = \frac{F}{a_2}$, we find $m_1 = \frac{2}{8} = 0.25 	ext{ kg}$ and $m_2 = \frac{2}{15} \approx 0.133 	ext{ kg}$. The total mass when combined is $m_{total} = m_1 + m_2 = \frac{1}{4} + \frac{2}{15} = \frac{15 + 8}{60} = \frac{23}{60} 	ext{ kg}$.

Working Principle: Newton's Second Law of Motion states that the force applied on an object is directly proportional to the product of its mass and acceleration. When two objects are tied together, their total inertia is the sum of their individual masses, assuming the combined system remains a single rigid body under the influence of the same external force.

Key Formulas: $F = m \cdot a$ — Newton's second law where $F$ is force, $m$ is mass, and $a$ is acceleration.; $m_{total} = m_1 + m_2$ — Sum of masses for combined objects.

Key Points: Newton's Second Law is the governing principle for motion under force.; Mass is an additive quantity in classical mechanics.; Units must be consistent; here $F$ is in Newtons and $a$ is in $m/s^2$, resulting in mass in $kg$.

Advantages: Provides a simple method to calculate the mass of unknown objects using basic dynamics.

Disadvantages: Neglects the mass of the connecting material (like rope or glue) used to tie the objects.

Applications: Calculating total payload in physics experiments.; Understanding vehicle dynamics when towing.

Additional Info: Individual calculation: $m_1 = \frac{2}{8} = \frac{1}{4} 	ext{ kg}$, $m_2 = \frac{2}{15} 	ext{ kg}$.. Sum: $\frac{1}{4} + \frac{2}{15} = \frac{15 + 8}{60} = \frac{23}{60} 	ext{ kg}$.

Answer: D is correct — The total mass of the system is the algebraic sum of the individual masses $m_1$ and $m_2$, resulting in $\frac{23}{60} 	ext{ kg}$.

Exam Tip: Always simplify your fractions early or find a common denominator immediately when working with physical quantities in multiple choice questions to save time.

Examoogle · Answer

Option A: $\frac{10}{40} 	ext{ kg}$

Examoogle · Answer

Option B: $\frac{3}{10} 	ext{ kg}$

Examoogle · Answer

Option C: $\frac{4}{10} 	ext{ kg}$

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