Two wheels `A` and `C` are connected by a belt `B` as shown in figure. The radius of `C` is three times the radius of `A`. What would be the ratio of the rotational inertias `(I_(C)//I_(A))` if both the wheels have the same rotational kinetic energy?

Answer

`09.00 `

Explanation

As the belt does not slip, `v_p = v_Q` İ.e., `r_A omega_A = r_C omega_C .... (because v = r omega).....(i)`
if `r_A = r,` then `r_C = 3r`
`therefore omega_A = 3 omega_C .....`[From (i)]
If both the wheels have the same rotational kinetic energy, then
`1/2 I_A omega_A^2 = 1/2 I_C omega_C^2`
`(I_C)/(I_A) = [(omega_A)/(omega_B)]^2 = [3/1]^2 = 9/1`