Question

A ball is whirled on the end of a string in a horizontal circle of radius R at constant speed v. Which way(s) can increase the centripetal acceleration of the ball by a factor of 9?

A) increasing both the radius and the speed by a factor of 9
B) Keeping the speed fixed and decreasing the radius by a factor of 9
C) Keeping the radius fixed and increasing the speed by a factor of 9
D) Keeping the speed fixed and increasing the radius by a factor of 9
E) decreasing both the radius and the speed by a factor of 9
F) Keeping the radius fixed and increasing the speed by a factor of 3

Answer 1

A, B and F are the right answers

Step-by-step explanation:

The formula is
`a_(c) = v^(2) / r`

A) Increasing both the radius and the speed by a factor of 9

`a_(c) = (9v)^(2) / (9r)` =
`9v^(2) / r`

which means the acceleration will increase by a factor of 9

B) Keeping the speed fixed and decreasing the radius by a factor of 9

`a_(c) = (v)^(2) / (r/9)` =
`9v^(2) / r`

which means the acceleration will increase by a factor of 9

C) Keeping the radius fixed and increasing the speed by a factor of 9

`a_(c) = (9v)^(2) / (r)` =
`81v^(2) / r`

It will increase the acceleration 81 times

D) Keeping the speed fixed and increasing the radius by a factor of 9

`a_(c) = (v)^(2) / (9r)` =
`v^(2) / 9r`

It will decrease the acceleration by 9 times

E) decreasing both the radius and the speed by a factor of 9

`a_(c) = (v/9)^(2) / (r/9)` =
`v^(2) / 9r`

It will decrease the acceleration by 9 times

F) Keeping the radius fixed and increasing the speed by a factor of 3

`a_(c) = (3v)^(2) / (r)` =
`9v^(2) / r`

It will increase the acceleration by 9 times