Question 26

A ball will experience the greatest acceleration when a 200 Newton force is applied to a 50 g ball.

The acceleration of an object is determined by Newton's second law of motion, which states that acceleration equals force divided by mass (a = F/m). In this case, the scenario that produces the highest acceleration involves the smallest mass with the largest force applied.

A) A 100 Newton force is applied to a 100 g ball.

In this case, the mass of the ball is 100 grams (0.1 kg). The acceleration can be calculated using the formula a = F/m, resulting in a = 100 N / 0.1 kg = 1000 m/s². While this is a significant acceleration, it is not the highest among the options provided.

B) A 100 Newton force is applied to a 175 kg ball.

Here, the ball has a mass of 175 kg. Using the same formula, the acceleration is a = 100 N / 175 kg = 0.57 m/s². This is the lowest acceleration among all the options due to the high mass relative to the applied force.

C) A 200 Newton force is applied to a 250 g ball.

For this option, the ball has a mass of 250 grams (0.25 kg). The acceleration can be calculated as a = 200 N / 0.25 kg = 800 m/s². Although this is a high acceleration, it is still less than that calculated for option D.

D) A 200 Newton force is applied to a 50 g ball.

In this scenario, the mass of the ball is 50 grams (0.05 kg). Applying the acceleration formula gives a = 200 N / 0.05 kg = 4000 m/s², which is the highest acceleration among all the options due to the combination of a large force and a small mass.

Conclusion

The correct answer is option D, where a 200 Newton force is applied to a 50 g ball, resulting in the greatest acceleration of 4000 m/s². This is significantly higher than the accelerations calculated for the other options, which either had higher masses or lower forces, thus demonstrating that a smaller mass paired with a larger force yields the highest acceleration.