Two cars having masses m1 and m2 move in circles of radii r1 and r2 respectively. If they complete the circles in equal time, the ratio of their angular speeds ω1 / ω2 is

Question

Two cars having masses m1 and m2 move in circles of radii r1 and r2 respectively. If they complete the circles in equal time, the ratio of their angular speeds ω1 / ω2 is (A) m1 / m2 (B) r1 / r2 (C) m1 r1 / m2 r2 (D) 1

Tardigrade Admin · Accepted Answer

T1=T2 (2 π r1/v1)=(2 π r2/v2) ⇒ (v1/r1)=(v2/r2) or ω1=ω2 ⇒ (ω1/ω2)=1

Q. Two cars having masses $m_{1}$ and $m_{2}$ move in circles of radii $r_{1}$ and $r_{2}$ respectively. If they complete the circles in equal time, the ratio of their angular speeds $ω_{1} / ω_{2}$ is

$m_{1} / m_{2}$

$r_{1} / r_{2}$

$m_{1} r_{1} / m_{2} r_{2}$

$1$

$T_{1} = T_{2}$
$\frac{2 π r _{1}}{v _{1}} = \frac{2 π r _{2}}{v _{2}}$
$\Rightarrow \frac{v _{1}}{r _{1}} = \frac{v _{2}}{r _{2}}$
or $ω_{1} = ω_{2}$
$\Rightarrow \frac{ω _{1}}{ω _{2}} = 1$

Q. Two cars having masses m1​ and m2​ move in circles of radii r1​ and r2​ respectively. If they complete the circles in equal time, the ratio of their angular speeds ω1​/ω2​ is

m1​/m2​

r1​/r2​

m1​r1​/m2​r2​

1

T1​=T2​ v1​2πr1​​=v2​2πr2​​ ⇒r1​v1​​=r2​v2​​ or ω1​=ω2​ ⇒ω2​ω1​​=1

Q. Two cars having masses $m_{1}$ and $m_{2}$ move in circles of radii $r_{1}$ and $r_{2}$ respectively. If they complete the circles in equal time, the ratio of their angular speeds $ω_{1} / ω_{2}$ is

$m_{1} / m_{2}$

$r_{1} / r_{2}$

$m_{1} r_{1} / m_{2} r_{2}$

$1$

$T_{1} = T_{2}$
$\frac{2 π r _{1}}{v _{1}} = \frac{2 π r _{2}}{v _{2}}$
$\Rightarrow \frac{v _{1}}{r _{1}} = \frac{v _{2}}{r _{2}}$
or $ω_{1} = ω_{2}$
$\Rightarrow \frac{ω _{1}}{ω _{2}} = 1$