A mass m is attached to a string and is whirled in a horizontal circle. If the radius of the circle is halved, what happens to the tension in the string if the speed remains constant?
Practice Questions
1 question
Q1
A mass m is attached to a string and is whirled in a horizontal circle. If the radius of the circle is halved, what happens to the tension in the string if the speed remains constant?
It doubles
It remains the same
It halves
It quadruples
Tension T = mv²/r. If r is halved, T doubles for constant speed.
Questions & Step-by-step Solutions
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Q
Q: A mass m is attached to a string and is whirled in a horizontal circle. If the radius of the circle is halved, what happens to the tension in the string if the speed remains constant?
Solution: Tension T = mv²/r. If r is halved, T doubles for constant speed.
Steps: 7
Step 1: Understand the formula for tension in the string, which is T = mv²/r.
Step 2: Identify the variables in the formula: T is tension, m is mass, v is speed, and r is the radius of the circle.
Step 3: Note that the problem states the speed (v) remains constant.
Step 4: Recognize that if the radius (r) is halved, we replace r with r/2 in the formula.
Step 5: Substitute r/2 into the formula: T = mv²/(r/2).
Step 6: Simplify the equation: T = mv² * (2/r) = 2(mv²/r).
Step 7: Conclude that the new tension (T) is double the original tension when the radius is halved and speed is constant.
