Which of the following correctly gives the relationship between linear speed V and angular speed ω of a body moving uniformly in a circle of radius r?

The correct relationship between linear speed V and angular speed ω of a body moving uniformly in a circle of radius r is, V = ωr. This equation means that the linear speed of an object moving in a circle is directly proportional to its angular speed and the radius of the circle. In other words, the larger the angular speed or the radius of the circle, the faster the object moves in a linear path. To understand this relationship, consider a point on a rotating wheel of radius r. As the wheel rotates, the point moves in a circle of circumference 2πr with an angular speed ω. If the point completes one full revolution in a time of T seconds, then its angular speed is ω = 2π/T. The linear speed V of the point is the distance it travels in a unit time, which is the circumference of the circle divided by the time taken to complete one revolution. Thus, V = 2πr/T. We can substitute the expression for ω in terms of T in the above equation to get V = ωr, which is the correct relationship between linear speed and angular speed for a body moving uniformly in a circle of radius r.