Two particles of equal mass are revolving with the same linear speed on circular paths of $r_{1} a n d r_{2}$ . The ratio of their angular velocity is ____.

\frac{r_{2}}{r_{1}}

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\sqrt{\frac{r_{2}}{r_{1}}}

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{(\frac{r_{1}}{r_{2}})}^{2}

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{(\frac{r_{2}}{r_{1}})}^{2}

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Solution

The correct option is A $\frac{r_{2}}{r_{1}}$
Linear velocity of $1^{s t}$ particle $= V_{1}$
Linear velocity of $2^{n d}$ particle $= V_{2}$
Now,
$V_{1} = V_{2}$
Angular velocity of $1^{s t}$ particle $= ω_{1}$
Angular velocity of $2^{n d}$ particle $= ω_{2}$
And, $ω = \frac{V}{r}$
$∴ \frac{ω_{1}}{ω_{2}} = \frac{V_{1}}{r_{1}} \times \frac{r_{2}}{V_{2}} = \frac{r_{2}}{r_{1}}$

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If the sum of the areas of two circles with radii $R_{1}$ and $R_{2}$ is equal to the area of a circle of radius R then

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Q. Question 1
If the sum of the areas of two circles with radii

R_{1}

and

R_{2}

is equal to the areas of a circle of radius R, then:
(A)

R_{1} + R_{2} = R

(B)

R_{1}^{2} + R_{2}^{2} = R^{2}

(C)

R_{1} + R_{2} < R

(D)

R_{1}^{2} + R_{2}^{2} < R_{2}

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Two particles of equal mass are revolving with the same linear speed on circular paths of r1and r2. The ratio of their angular velocity is ____.

The correct option is A r2r1Linear velocity of 1st particle =V1Linear velocity of 2nd particle =V2Now,V1=V2Angular velocity of 1st particle =ω1Angular velocity of 2nd particle =ω2And, ω=Vr∴ω1ω2=V1r1×r2V2=r2r1

Two particles of equal mass are revolving with the same linear speed on circular paths of $r_{1} a n d r_{2}$ . The ratio of their angular velocity is ____.