Question

Suppose we are told that the acceleration of a particle moving with uniform speed V in a ˚le of radius r is proportional to some power r, say r raised to power n, and some of V, say B to power m. Determine the values of n and m and write the simplest form of an equation for the acceleration of Y.

A) n = 1, m = 2; a=r+v^2
B) n = 2, m = 1; a=r^2+V
C) n = 0, m = 2; a=V^2
D) n = 1, m = 1; a=r+V

Answer 1

The correct values are n = 0 and m = 2, which indicates that the acceleration is proportional to the square of the velocity (V²) and not directly proportional to the radius, confirming option C as the right answer.

Step-by-step explanation:

The question refers to a particle moving with a uniform speed V in a circle of radius r and asks us to determine the power n of the radius and the power m of the speed which the centripetal acceleration (a) is proportional to. Using the formulas for centripetal acceleration (a = V²/r), we can say that the acceleration is directly proportional to the square of the velocity (V²) and inversely proportional to the radius (r). Therefore, r is raised to the power of -1, not n, and V is raised to the power of 2, making m equal to 2. This makes option C, n = 0 and m = 2; a = V², the correct choice because the acceleration is proportional to the square of the velocity and not directly proportional to the radius at all.