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Question

The ratio of orbital speeds of two satellites, if the ratio of their time period is 8:1 are

A
(VO)1(VO)2=41
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B

(VO)1(VO)2=12
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C
(VO)1(VO)2=14
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D

(VO)1(VO)2=21
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Solution

The correct option is B
(VO)1(VO)2=12
Orbital speed of a satellite is given by,

VO=GMr

(VO)1=GMr1

(VO)2=GMr2

(VO)1(VO)2=GMr1×r2GM

(VO)1(VO)2=r2r1 .....(1)

The period of revolution of a satellite is given by,

T2r3(T1T2)2=(r1r2)3

T1T2=81(r1r2)3=(81)2

r1r2=41r2r1=14 .......(2)

Using equation (1) and (2) we have,

(VO)1(VO)2=14=12

Hence, option (B) is the correct answer.

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