Question

two different artificial satellites orbiting with same time period around the earth having angular movementa in 2:1`.the ratio of masses of the satellites will be

Answer 1

ratio of masses of the satellite will be 2 : 1

time period of artificial satellite is given as , T = 2π√{r³/GM}

where, M is mass of the earth and r is the radius of path where satellite is orbiting.

as time period of different satellites are equal so, r will be same for both satellites.

i.e., r1/r2 = 1/1 ......(1)

now angular momentum , L = mr²ω

well, ω ∝ 1/T so, ω1/ω2 = 1/1

now, L1/L2 = (m1/m2)(r1/r2)²(ω1/ω2)

⇒2/1 = (m1/m2) × (1/1)² × (1/1)

⇒m1/m2 = 2/1

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Answer 2

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

time period of artificial satellite is given as , T = 2π√{r³/GM}

where, M is mass of the earth and r is the radius of path where satellite is orbiting.

as time period of different satellites are equal so, r will be same for both satellites.

i.e., r1/r2 = 1/1 ......(1)

now angular momentum , L = mr²ω

well, ω ∝ 1/T so, ω1/ω2 = 1/1

now, L1/L2 = (m1/m2)(r1/r2)²(ω1/ω2)

⇒2/1 = (m1/m2) × (1/1)² × (1/1)

⇒m1/m2 = 2/1