Question

two satellites of two different planets are of equal masses.They revolve in orbits if radius in the ratio 1:3,with same time period.Then.
1)linear speed ratio1:8
2) acceleration in the ratio 1:9
3)Angular speed equal
4)linear speed in the ratio1:9
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Answer 1

answer : option (3) angular speed equal.

let mass of first planet is m1 and mass of the other planet is m2.

linear speed of first satellite, v1 = √(Gm1/r1)

linear speed of 2nd satellite, v2 = √(Gm2/r2)

as it is given that,

time period of both satellites are same.

so, T1 = T2

⇒√(r1³/Gm1) = √(r2³/Gm2)

⇒r1³/m1 = r2³/m2

⇒m1/m2 = (r1/r2)³

as it is given , r1/r2 = 1 /3

so, m1/m2 = (1/3)³ = 1/27

now, ratio of their linear speeds = v1/v2 = √{(m1/m2) × (r2/r1)}

= √{(1/27) × (3/1)} = 1/3

ratio of their accelerations = a1/a2 = (v1²/r1)/(v2²/r2) = (v1/v2)² × (r2/r1)

= (1/3)² × (3)

= 1/3

ratio of angular speeds = w1/w2 = (2π/T1)/(2π/T2)

= T2/T1 = 1 [given, T1 = T2]

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Answer 2

$\huge\bold\purple{Answer:-}$

(3) angular speed equal.