Two racing cars of masses `m_(1)` and `m_(2)` are moving in circles of radii `r_(1)` and `r_(2)` respectively. Their speeds are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is

Options

A. `m_(1): m_(2)`
B. `r_(1):r_(2)`
C. `1:1`
D. `m_(1)r_(1):m_(2)`

Answer

C

Explanation

Speed `V_(1) = (2pi r_(1))/(t)`
`V_(2) = (2pi r_(2))/(t)`
`omega_(1)=(V_(1))/(r_(1))=(2pi)/(t)implies omega_(2)=(V_(2))/(r_(2))=(2pi)/(t)`
`omega_(1)= omega_(2) implies (omega_(1))/(omega_(2))=(I)/(I)`