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 _______

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Solution

The correct option is D
1

$ω_{1} = \frac{△ θ}{△ t}$

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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Two cars having masses m1 and m2 move in circles of radii r1 and r2 respectively. If they complete the circle in equal time, the ratio of their angular speeds ω1ω2 is _______

The correct option is D 1 ω1=△θ△t If time taken to complete a revolution is t. Then ω1=2πt,ω2=2πt ⇒t=2πω1=2πω2 ⇒ we get ω1=ω2 or ω1ω2=1

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 _______

The correct option is D
1

$ω_{1} = \frac{△ θ}{△ t}$

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