A 1.2m dimater hoop with ....

Question

A 1.2 m diameter hoop with moment of inertia, Ih = Mr^2, starts from rest at a height 1.2 m above the base of an inclined plane and rolls down (without slipping) to the bottom. What is the linear speed of the hoops center of mass just as the hoop leaves the bottom of the incline?

a. 11.76 m/s

b. 4.84 m/s

c. 3.34 m/s 

d. 2.42 m/s

(Correct answer is C, 3.34 m/s)

Answer 1

Mv²/2 + Iω²/2 = Mgh

 

Mv²/2 + (Mr²)(v/r)²/2 = Mgh

 

v²(1/2 + 1/2) = gh

 

v = √(gh) = √[9.8(1.2)] m/s ≅ 3.43 m/s

 

Student, I think there is a typo in answer (c), and that it should say 3.43 m/s.  Please check.