Question

If two objects move in a circular path of radii in the ratio of 1:3 and take same time to complete the circle , what is the ratio of their speed ?

Answer 1

Time taken by object one =Distance/time taken=2pi(r₁)/s₁
Time taken by obect two=Distance/time taken=2pi(r₂)/s₂

since r₁:r₂=1:3
=>r₂=3r₁

T₁=T₂
=>2pi(r₁)/s₁=2pi(3r₁)/s₂

=>s₁/s₂=1/3

Therefore,the ratio of the speeds is 1:3

Answer 2

Concept:

• Uniform circular motion
• Calculating speed
• Calculating the perimeter of a circle

Given:

• Ratio of circular paths r1/r2 = 1/3
• Let r1 = r
• Let r2 = 3r
• Both objects take the same time = t to complete the circle

Find:

• The ratio of the speeds of the objects

Solution:

The distance covered by the objects is equal to the perimeter or circumference of the circle which is 2πR.

Distance covered by the first object s1 =  2πr1 =  2πr

Distance covered by the second object s2 =  2πr2 =  2π3r = 6πr

Speed = distance/time

Speed of the first object v1 = s1/t = 2πr/t

Speed of the second object v2 = s2/t = 6πr/t

V1/v2 = (2πr/t)/ (6πr/t) = 1/3

The ratio of their speeds is 1:3.

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