Question

A stone whirled on a string experiences a centripetal acceleration of 10 m/s². If the string were shortened to half its length (one-half the radius) and the speed were doubled, what would be the centripetal acceleration?

Options:
A) 5 m/s²
B) 10 m/s²
C) 20 m/s²
D) 40 m/s²

Answer 1

The centripetal acceleration would be 40 m/s².

Step-by-step explanation:

To calculate the centripetal acceleration when the speed is doubled and the radius is halved, we can use the formula:

ac = (v^2) / r

Given that the initial centripetal acceleration is 10 m/s², if the speed is doubled and the radius is halved, the new centripetal acceleration can be calculated as:

ac' = (2v)^2 / (r/2)

Substituting the values, we get:

ac' = (4v^2) / (r/2) = 4(v^2 / r) = 4(10 m/s²) = 40 m/s²

Therefore, the centripetal acceleration would be 40 m/s². Option D) 40 m/s² is the correct answer.