Question: A body is moving in a circular path of radius 4 m with a constant speed of 8 m/s. What is the net force acting on the body if its mass is 2 kg?
Options:
4 N
8 N
16 N
32 N
Correct Answer: 16 N
Solution:
Centripetal force F = m(v²/r) = 2(8²/4) = 32 N.
A body is moving in a circular path of radius 4 m with a constant speed of 8 m/s
Practice Questions
Q1
A body is moving in a circular path of radius 4 m with a constant speed of 8 m/s. What is the net force acting on the body if its mass is 2 kg?
4 N
8 N
16 N
32 N
Questions & Step-by-Step Solutions
A body is moving in a circular path of radius 4 m with a constant speed of 8 m/s. What is the net force acting on the body if its mass is 2 kg?
Correct Answer: 32 N
Step 1: Identify the given values. The mass (m) of the body is 2 kg, the speed (v) is 8 m/s, and the radius (r) of the circular path is 4 m.
Step 2: Use the formula for centripetal force, which is F = m(v²/r). This formula helps us find the net force acting on an object moving in a circle.
Step 3: Calculate v² (the speed squared). Here, v = 8 m/s, so v² = 8 * 8 = 64 m²/s².
Step 4: Divide v² by the radius (r). We have r = 4 m, so 64 m²/s² divided by 4 m equals 16 m/s².
Step 5: Multiply the result by the mass (m). We have m = 2 kg, so 2 kg * 16 m/s² = 32 N.
Step 6: Conclude that the net force acting on the body is 32 N.
Centripetal Force – The net force required to keep an object moving in a circular path, directed towards the center of the circle.
Newton's Second Law – The relationship between force, mass, and acceleration, which is applied here to derive the centripetal force.
Uniform Circular Motion – Motion in a circular path at a constant speed, where the direction of the velocity vector changes continuously.
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