Problem: A wheel with a rubber tire has an outside diameter of 25 in . When the radius has been decreased a quarter of an inch, the number of revolutions of the wheel in one mile will:
Answer Choices:
A. be increased about 2%
B. be increased about 1%
C. be increased about 20%
D. be increased by 1/2%
E. remain the same
Solution:
N1β=ΟD1 mile β,N2β=Ο[Dβ(1/2)]1 mile β,N2ββN1β=Ο1 mile ββ
D[Dβ(1/2)]1/2β.
β΄N1βN2ββN1ββ=Dβ1/21/2β=2421β1/2β=491β;
β΄ the percent increase is 100β
491ββΌ2%.