Two racing cars of masses m1 and m2 are moving in circles of radii r1 and r2 respectively. Their speeds are such that each makes a complete circle in the same time t . The ratio of the angular speeds of the first to the second car is

Question

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

Tardigrade Admin · Accepted Answer

We know that Angular velocity = ( text Angular diaplacoment(θ)/ textTime) As both cars complete their circle (2π) in equal time ω1 = (2π/t) ....(i) ω2 = (2π/t) ...(ii) From Eqs. (i) and (ii), we get (ω1/ω2) = (1/1)

Q. 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 time $t$ . The ratio of the angular speeds of the first to the second car is

$r_{1} : r_{2}$

$m_{1} : m_{2}$

$1 : 1$

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

We know that
Angular velocity $= \frac{Angular diaplacoment ( θ )}{Time}$
As both cars complete their circle $(2 π)$ in equal time
$ω_{1} = \frac{2 π}{t} .... (i)$
$ω_{2} = \frac{2 π}{t} ... (ii)$
From Eqs. $(i)$ and $(ii)$ , we get
$\frac{ω _{1}}{ω _{2}} = \frac{1}{1}$

Q. Two racing cars of masses m1​ and m2​ are moving in circles of radii r1​ and r2​ respectively. Their speeds are such that each makes a complete circle in the same time t . The ratio of the angular speeds of the first to the second car is

r1​:r2​

m1​:m2​

1:1

m1​m2​:r1​r2​