Question

Two bodies are moving on two different circular tracks with the same speed . if the ratio of radii of circular tracks is 2:1 then their respective angular speeds are in ratio of
a. 1:1 b. 2:1 c. 1:2 d. 1:4​

Answer 1

Given :-

Two bodies are moving on two different circular tracks with the same speed

Ratio of radii = 2 : 1

To Find :-

Ratio of angular speeds of the bodies

Solution :-

the rate of change of angular position of body moving in a circular path is called Angular velocity

Angular velocity is a vector quantity, which have both direction and magnitude.

Angular velocity of a body moving is given by

• ω = v/r

here, ω denotes Angular velocity, v denotes speed and r denotes radius.

According to Question,

➠ r₁ω₁ = r₂ω₂ ⠀⠀⠀⠀⠀⠀⠀⠀.i.e.,

➠ r₁/r₂ = ω₂/ω₁

➠ 2/1 = ω₂/ω₁

➠ ω₁:ω₂ = 1:2

thus, the ratio of angular speeds of the bodies is 1:2

hence, option 3 is right$.$

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#sanvi….

Answer 2

Solution :-

As per the given data ,

• r : r ' = 2 : 1

Angular velocity

➥The rate of change of angular displacement with respect to time

➥It is a vector quantity

➥The direction of angular velocity is perpendicular to the plane of rotation

Angular velocity  is given by ,

➨ ω = v / r

From this we can conclude that  ,

➨ ω ∝ 1 / r

Hence ,

➨ ω / ω ' = r ' / r

Now let's substitute the given values in the above equation ,

➨ ω / ω ' = 1 / 2

The ratio of their angular speeds is 1 :2