A round object of mass 10 kg and radius 0.5 m rolls without slipping down a hill from a height of 4.5 m. If its speed at the bottom is 6.5 m/s, what is the moment of inertia of the object about its center? a) 4.79 kg·m2 b) 3.63 kg·m2 c) 2.72 kg·m2 d) 2.34 kg·m2 e) 2.00 kg·m2

moment of inertia is 2.72 kg m²

Explanation:

given data

mass m = 10kg

height h = 4.5 m

radius r = 0.5 m

speed v = 6.5 m/s

to find out

moment of inertia

solution

we apply here conservation of energy

that is

mgh = 1/2 * mv² + 1/2 * Iω²

here I is moment of inertia we find and

we know ω = Velocity / radius = 6.5 / 0.5 = 13

and g = 9.8

so put here all these value

10 (9.8) 4.5 = 1/2 * (10) (6.5) ² + 1/2 * I (13) ²

441 = 211.25 + 1/2 * I (169)

I = 2.72

so moment of inertia is 2.72 kg m²