Two wheels are connected by a belt. The radius of the larger wheel is three times that of the smaller one. What is the ratio of the moment of inertia of larger wheel to the smaller wheel, when both wheels have same angular momentum?

Options

A. 3
B. 6
C. 9
D. 12

Answer

A

Explanation

As the belt does not slip , `v_(A) = v_(B)`
or `r_A omega _A = r_(B) omega_(B) or (omega_(A))/(omega_(B)) = (r_(B))/(r_(A)) = 3`
If both the wheels have same angular momentum , then `I_(A) omega_(A) = I_(B) omega_(B) or (I_(B))/(I_(A)) = (omega_(A))/(omega_(B)) = 3`