Answer
The radius of the first pully is $r_1$, of the secund pully it is $r_2$.
The angular speed of the first pully is $\omega_1$, of the secund pully it is $\omega_2$.
The linear speeds of the pullys are equal, hence $v_1=v_2\\r_1\omega_1=r_2\omega_2\\\frac{r_1}{r_2}=\frac{omega_1}{omega_2}$
Thus we proved what we wanted to.
Work Step by Step
The radius of the first pully is $r_1$, of the secund pully it is $r_2$.
The angular speed of the first pully is $\omega_1$, of the secund pully it is $\omega_2$.
The linear speeds of the pullys are equal, hence $v_1=v_2\\r_1\omega_1=r_2\omega_2\\\frac{r_1}{r_2}=\frac{omega_1}{omega_2}$
Thus we proved what we wanted to.
