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Gravitation question

2021 · 24 Feb · Shift 1 · Q55
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  5. /2021 · 24 Feb · Shift 1 · Q55

Gravitation question

2021 · 24 Feb · Shift 1 · Q55

JEE MainPhysicsGravitationMCQ+4 / −1
Consider two satellites S1 and S2 with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S1 to the angular velocity of satellite S2 is :
  1. A
    1 : 4
  2. B
    8 : 1
  3. C
    2 : 1
  4. D
    1 : 8
View written solutionFree

Correct answer: B

  1. Use the relation between angular velocity and time period

For uniform circular motion,

ω=2πT\omega = \frac{2\pi}{T}ω=T2π​

where ω\omegaω is angular velocity and TTT is the time period.

  1. Write angular velocities for both satellites

For satellite S1S_1S1​:

T1=1 hrT_1 = 1\ \text{hr}T1​=1 hr

so,

ω1=2πT1=2π1\omega_1 = \frac{2\pi}{T_1} = \frac{2\pi}{1}ω1​=T1​2π​=12π​

For satellite S2S_2S2​:

T2=8 hrT_2 = 8\ \text{hr}T2​=8 hr

so,

ω2=2πT2=2π8\omega_2 = \frac{2\pi}{T_2} = \frac{2\pi}{8}ω2​=T2​2π​=82π​
  1. Find the ratio
ω1ω2=2π12π8=8\frac{\omega_1}{\omega_2} = \frac{\frac{2\pi}{1}}{\frac{2\pi}{8}} = 8ω2​ω1​​=82π​12π​​=8

Hence,

ω1:ω2=8:1\omega_1 : \omega_2 = 8 : 1ω1​:ω2​=8:1
  1. Match with the options

The correct option is: B: 8:18:18:1

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