Answer:
Option D: Four times the original speed.
Explanation:
A centripetal force accelerates a body by changing the direction of the body's velocity without changing the body's speed.
The speed(v) is therefore constant, thereby making the magnitudes of the of the acceleration and the force constant.
The formula used to calculate the Centripetal force is given below:
[tex]F = \frac{mv^2}{r}[/tex]
where F represents the Centripetal force, m represents the mass of the moving body, v represents the speed or velocity at which the body is moving and r represents the radius.
Making the speed the subject of the formula: [tex]v^{2} = \frac{rF}{m} \\[/tex]
Therefore, when the radius (r) is changed to 4r, i.e r = 4r
speed(v) becomes [tex]v^2 = \frac{4rF}{m}[/tex]
After comparing, the difference between the speeds is Four times the original speed.
