Question

A ball attached to a string is whirled around in a horizontal circle having a radius r. If the radius of the circle is changed to 4r and the same centripetal force is applied by the string, the new speed of the ball is which of the following?a. One-quarter the original speed

b. Twice the original speed
c. One-half the original speed
d. Four times the original speed

Answer 1

The new speed of the ball when the radius is changed to 4r and the same centripetal force is applied by the string will be one-half the original speed.

Step-by-step explanation:

The new speed of the ball when the radius of the circle is changed to 4r and the same centripetal force is applied by the string will be one-half the original speed.

Centripetal force is given by the equation Fc = mv²/r, where Fc is centripetal force, m is the mass of the ball, v is the velocity, and r is the radius of the circle. When the radius is changed to 4r, the centripetal force remains the same. Therefore, the velocity of the ball must decrease by half in order to maintain the same centripetal force.

For example, if the original speed of the ball was 10 m/s, the new speed would be 5 m/s.

Answer 2

Option D: Four times the original speed.

Step-by-step 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:

`F = (mv^2)/(r)`

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:
`v^(2) = (rF)/(m) \\`

Therefore, when the radius (r) is changed to 4r, i.e r = 4r

speed(v) becomes
`v^2 = (4rF)/(m)`

After comparing, the difference between the speeds is Four times the original speed.