If a stone is tied to a string and whirled in a horizontal circle of radius 2 m
Practice Questions
Q1
If a stone is tied to a string and whirled in a horizontal circle of radius 2 m at a speed of 4 m/s, what is the tension in the string if the mass of the stone is 1 kg?
2 N
4 N
8 N
10 N
Questions & Step-by-Step Solutions
If a stone is tied to a string and whirled in a horizontal circle of radius 2 m at a speed of 4 m/s, what is the tension in the string if the mass of the stone is 1 kg?
Step 1: Identify the given values. The mass of the stone (m) is 1 kg, the speed (v) is 4 m/s, and the radius (r) is 2 m.
Step 2: Use the formula for centripetal force, which is F = m(v²/r). This formula helps us find the force needed to keep the stone moving in a circle.
Step 3: Calculate v² (the speed squared). Here, v = 4 m/s, so v² = 4 * 4 = 16 m²/s².
Step 4: Divide v² by r (the radius). We have v² = 16 m²/s² and r = 2 m, so 16 / 2 = 8 m/s².
Step 5: Multiply the result by the mass (m). We have m = 1 kg, so the centripetal force is 1 kg * 8 m/s² = 8 N.
Step 6: The tension in the string is equal to the centripetal force needed to keep the stone moving in the circle, which is 8 N.
Centripetal Force – The force required to keep an object moving in a circular path, directed towards the center of the circle.
Tension in a String – The force exerted by a string when it is pulled tight by forces acting from opposite ends.
Newton's Second Law – The relationship between the force acting on an object, its mass, and its acceleration (F = ma).
