Question

A physics student is performing a lab in which she twirls a rubber stopper at the end of a string around in a circle at nearly constant speed and tries to determine its acceleration.
Which of the following single changes would enable her to most nearly double the acceleration of the rubber stopper?

• A. Double the speed of the rubber stopper
• B. Use a string that is twice as long as the original string
• C. Reduce the speed of the rubber stopper to half its original value
• D. Use a string that is half as long as the original string
• E. Use a rubber stopper with twice as much mass as the original rubber stopper

Answer 1

Answer: (D)

Use a string that is half as long as the original string

As the speed of rubber stopper is constant so its tangential acceleration will be zero , and total acceleration will be equal to the centripetal acceleration only .

centripetal acceleration $a$ of rubber stopper , moving with velocity $v$ in a circular path of radius $r$ is given by ,

$a=v^2/r$

or $a\propto v^2$ and $a\propto 1/r$

so if we ,

double the speed $v$ , $a$ will be $4a$ ,

use a string of double length $2r$ , $a$ will be $a/2$ ,

reduce the speed to $v/2$ , $a$ will be $a/4$ ,

use a string of half length $r/2$ , $a$ will be $2a$ ,

mass has no effect on acceleration , option D is correct .