Question

multiple choice
what is the relationship between mass and acceleration?
a both increase when force is applied
b when one increases, the other one also increases
c when one increases, the other one decreases
d both decrease when force is applied

Explanation:

To determine the relationship between mass and acceleration, we use Newton's second law of motion, which is given by the formula \( F = ma \) (where \( F \) is force, \( m \) is mass, and \( a \) is acceleration). If the force \( F \) is kept constant, we can rearrange the formula to \( a=\frac{F}{m} \). This shows that acceleration \( a \) is inversely proportional to mass \( m \) when force is constant. So, when mass (one quantity) increases, acceleration (the other quantity) decreases, and vice versa.

• Option A: Mass is an intrinsic property of an object and does not increase when a force is applied (force causes acceleration, not an increase in mass). So A is incorrect.
• Option B: From the inverse - proportional relationship (\( a=\frac{F}{m} \) with constant \( F \)), mass and acceleration do not increase together. So B is incorrect.
• Option C: As explained by \( a = \frac{F}{m} \) (constant \( F \)), when mass increases, acceleration decreases, and when mass decreases, acceleration increases. So this option correctly describes the inverse relationship between mass and acceleration when force is constant.
• Option D: Mass does not decrease when a force is applied, and acceleration (for a constant force and non - zero mass) is non - negative and related to mass inversely, not in a way that both decrease. So D is incorrect.

Answer:

C. when one increases, the other one decreases