g hoop rolls without slipping on a horizontal surface. The hoop has a mass m and radius r. What is the ratio of the hoop's translational kinetic energy to the hoop's rotational kinetic energy, KT /KR

Explanation:

The translational kinetic energy of the hoop is given as:

     ---------------------- equation (1)

where,

= translational kinetic energy

m = mass of hoop

v = linear speed of hoop

The rotational kinetic energy of the hoop is given as:

where,

= rotational kinetic energy of the hoop

I = Moment of Inertia of the hoop = mr²

r = radius of the hoop

ω = angular speed of hoop =

Therefore,

------------------- equation (2)

dividing equation (1) and equation (2), we get:

50 inches should be the resultant vector