Two cars having masses m1 and m2 move in circles of radii r1 and&

Question

Two cars having masses

m_{1} a n d m_{2}

move in circles of radii

r_{1} a n d r_{2}

respectively. If they complete the circle in equal time, the ratio of their angular speeds

\frac{ω_{1}}{ω_{2}}

is _______

Options:

A . m1m2

B . r1r2

C . m1r1m2r2

D . 1

Answer: Option D
:
D

ω_{1} = \frac{△ θ}{△ t}

If time taken to complete a revolution is t.
Then

ω_{1} = \frac{2 π}{t}, ω_{2} = \frac{2 π}{t}

\Rightarrow t = \frac{2 π}{ω_{1}} = \frac{2 π}{ω_{2}}

\Rightarrow

we get

ω_{1} = ω_{2} o r \frac{ω_{1}}{ω_{2}} = 1

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