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The question describes two masses, \( m \) and \( 2m \), being subjected to equal forces. We need to determine how their accelerations compare, based on Newton's second law of motion.

### Newton's Second Law:
\[
F = ma
\]
Where:
- \( F \) is the force applied,
- \( m \) is the mass,
- \( a \) is the acceleration.

For the first mass \( m \):
\[
F = m \cdot a_1 \quad \text{(where \( a_1 \) is the acceleration of mass \( m \))}
\]
Thus, the acceleration is:
\[
a_1 = \frac{F}{m}
\]

For the second mass \( 2m \):
\[
F = 2m \cdot a_2 \quad \text{(where \( a_2 \) is the acceleration of mass \( 2m \))}
\]
Thus, the acceleration is:
\[
a_2 = \frac{F}{2m}
\]

### Comparing the accelerations:
\[
\frac{a_2}{a_1} = \frac{\frac{F}{2m}}{\frac{F}{m}} = \frac{1}{2}
\]

This means the acceleration of the mass \( 2m \) is half that of mass \( m \).

### Conclusion:
The correct alternative is:
\[
\boxed{\text{b. the acceleration of mass } 2m \text{ is half that of mass } m.}
\]

Would you like further explanation or details? Here are some related questions:

1. What is Newton’s second law, and how does it apply to different masses?
2. How would the acceleration change if the forces on the two masses were not equal?
3. If the masses were subjected to different forces, how would you calculate the accelerations?
4. How does the relationship between force, mass, and acceleration help in understanding motion?
5. Can you give an example where two different masses are accelerated with the same force?

**Tip:** Whenever the force is constant, the acceleration is inversely proportional to the mass of the object. So, as the mass increases, acceleration decreases!

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

Explore how Newton's Second Law explains the relationship between force, mass, and acceleration. Given two masses m and 2m subjected to equal forces, learn why the acceleration of mass 2m is half that of mass m, and review key concepts of mass and acceleration. Suitable for Grades 9-12.

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