Question

Two bodies in a circular paths of radii 1:2 take same time ti complete theie circles .Find the ratio of their linear speed ?

Answer 1

here's your answer.....

Answer 2

Answer:

Ratio of linear speed of the two bodies = $1:2$

Explanation:

Given:

The ratio of radii of circular paths = 1 : 2

Time taken by the two bodies = t

Find:

The ratio of linear speed of the two bodies = ?

Solution:

Circular path 1:

The radius of the circular path = $r$

Circumference of the circular path = $2\pi r$

∴ Distance covered by the body = $2\pi r$

Time taken by the body = t

∴ Linear speed = $\frac{Distance \ covered }{Time \ taken}$

                         = $\frac{2\pi r}{t}$

Circular path 2:

The radius of the circular path = $2r$   (∵ ratio of radii = 1:2 )

Circumference of the circular path = $2\pi \times 2r = 4\pi r$

∴ Distance covered by the body = $4\pi r$

Time taken by the body = t

∴ Linear speed = $\frac{Distance \ covered }{Time \ taken}$

                         = $\frac{4\pi r}{t}$

Ratio of linear speed of the two bodies = $\frac{2\pi r}{t} : \frac{4\pi r}{t}$

Cancelling the common terms,

∴ Ratio of linear speed = $2:4=1:2$

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