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In this problem, you are asked to compare the accelerations of two masses, \( m \) and \( 2m \), subjected to equal forces.

The key equation to use is Newton's Second Law of Motion:
\[
F = ma
\]
where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration. 

Since the forces applied to both masses are the same, we can write:
\[
F = m a_1 \quad \text{and} \quad F = 2m a_2
\]
where \( a_1 \) is the acceleration of mass \( m \) and \( a_2 \) is the acceleration of mass \( 2m \).

Rearranging these equations to solve for acceleration, we get:
\[
a_1 = \frac{F}{m} \quad \text{and} \quad a_2 = \frac{F}{2m}
\]

Now, comparing the two accelerations:
\[
\frac{a_2}{a_1} = \frac{F/(2m)}{F/m} = \frac{1}{2}
\]

This shows that the acceleration of the mass \( 2m \) is half that of mass \( m \). Therefore, the correct answer is:
\[
\boxed{b}
\]

Would you like further details on this? 

Here are 5 related questions to deepen your understanding:
1. What happens to acceleration if the force is doubled for the same mass?
2. How does Newton's second law apply to objects moving in different directions?
3. What would be the effect on acceleration if the mass is tripled but the force stays the same?
4. How does friction impact acceleration when force is applied?
5. Can an object have zero acceleration while a force is applied?

**Tip**: Always remember that acceleration is inversely proportional to mass when force is constant.

A mass m and a mass 2m are subjected to equal forces. Choose an alternative: a) the acceleration of mass 2m is four times that of mass m b) the acceleration of mass 2m is half that of mass m c) their accelerations are equal d) the acceleration of mass 2m is double that of mass m

Learn how to calculate the acceleration of masses m and 2m subjected to equal forces using Newton's Second Law. This problem covers key concepts of force, mass, and acceleration, suitable for high school students (Grades 9-12).

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