Two racing cars of masses m1 and m2 are moving in a circles of radii r1 and r2 respectively. Their speeds are such that each makes a complete round of circle in the same internal of time. The ratio of their angular speeds are :

Question

Two racing cars of masses m1 and m2 are moving in a circles of radii r1 and r2 respectively. Their speeds are such that each makes a complete round of circle in the same internal of time. The ratio of their angular speeds are : (A)  m1m2: r1r2  (B) 1: 1 (C)  r1: r2  (D)  m2: m1

Tardigrade Admin · Accepted Answer

Angular velocity is the rate of change of angular displacement with time.
Given that both the cars complete one circle in the same time '

t

'
Angular speed

= ω = \frac{angle subtended by the car for one revolution ( 2 π )}{Time Taken( ( t )}

Angular speed of first car,

= ω_{1} = \frac{2 π}{t}

Angular speed of second car,

= ω_{2} = \frac{2 π}{t}

The ratio of angular speed of first car to that of second

= \frac{ω _{1}}{ω _{2}} = 1 : 1

Q. Two racing cars of masses $m_{1}$ and $m_{2}$ are moving in a circles of radii $r_{1}$ and $r_{2}$ respectively. Their speeds are such that each makes a complete round of circle in the same internal of time. The ratio of their angular speeds are :

$m_{1} m_{2} : r_{1} r_{2}$

$1 : 1$

$r_{1} : r_{2}$

$m_{2} : m_{1}$

Q. Two racing cars of masses m1​ and m2​ are moving in a circles of radii r1​ and r2​ respectively. Their speeds are such that each makes a complete round of circle in the same internal of time. The ratio of their angular speeds are :

m1​m2​:r1​r2​

1:1

r1​:r2​

m2​:m1​

Q. Two racing cars of masses $m_{1}$ and $m_{2}$ are moving in a circles of radii $r_{1}$ and $r_{2}$ respectively. Their speeds are such that each makes a complete round of circle in the same internal of time. The ratio of their angular speeds are :

$m_{1} m_{2} : r_{1} r_{2}$

$1 : 1$

$r_{1} : r_{2}$

$m_{2} : m_{1}$