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?

Answer 1

Answer:

twice the original speed

Explanation:

the centripetal force is the force of an object moving in a circle of turning and it is given by the expression

$F=\frac{mv^{2} }{r}$

where f = force of the object

          m = mass

         v = velocity

         r = radius of the circle

first we need to know what the orignal speed will be then we can tell what will happen if the radius of the circle is changed to 4R.

from the expression for the centripetal force, we need to make the velocity subject of the formula

$F = \frac{mv^{2} }{r} \\cross multiplying\\Fr =mv^{2} \\dividing both sides by m\\\frac{Fr}{m}=v^{2} \\taking the square root of both sides\\v=\sqrt{\frac{Fr}{m} }$

now, if the radius is changed to 4R

in the expression for v above i will need to just insert 4R in place of r

$v=\sqrt{\frac{4rF}{m} }$

the square root of 4 is 2,

therefore

$v=2\sqrt{\frac{rF}{m} }$

we can see that this is just twice of what the original speed was.