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) m1r1/m2r2
(d) 1

Answer 1

Answer ⇒ Option (d).  1

Mathematical Expression ⇒ As we know that  the angular velocity of the body is given by the relation,

     ω = 2π/T

From this expression it can made clear that angular velocity does not depends upon the mass of the body and also on the Radius of the body.

∴ If they are completing the Round in equal time then,

  T₁ = T₂

∴  ω₁ = 2π/T and ω₂ = 2π/T

∴ Ratio =  ω₁/ω₂  = 1/1 = 1

Hope it helps.

Answer 2

We know,

Angular speed is given by

ω = v/r

also, v = 2πr/T (for uniform circular motion)

Combining both equations

ω = 2π/T



For the both cars time period is same.

So,

ω1 / ω2 = T / T = 1 / 1

Hope this will help you......✌