Motion of a Satellite ( Orbital Velocity, Time Period and Energy of Satellite ) NEET Questions

Motion of a Satellite ( Orbital Velocity, Time Period and Energy of Satellite )

Motion of a Satellite ( Orbital Velocity, Time Period and Energy of Satellite ) MCQ Questions

7.
Two satellites S₁ and S₂ orbit Earth at heights h₁ and h₂ respectively where h₁ < h₂. Which of the following is true?
A.
V₁ < V₂ and T₁ > T₂
B.
V₁ > V₂ and T₁ < T₂
C.
V₁ > V₂ and T₁ > T₂
D.
V₁ < V₂ and T₁ < T₂
ANSWER :
B. V₁ > V₂ and T₁ < T₂
8.
The time period of a satellite in circular orbit of radius (R_E + h) around Earth is given by NCERT Eq. 7.37 as:
A.
T = 2π(R_E+h)/√(GM_E)
B.
T = 2π(R_E+h)^(3/2)/√(GM_E)
C.
T = 2π√(R_E+h)/GM_E
D.
T = (R_E+h)^(3/2)/√(GM_E)
ANSWER :
B. T = 2π(R_E+h)^(3/2)/√(GM_E)
9.
For a satellite very close to Earth's surface (h << R_E), the time period T₀ is:
A.
T₀ = 2π√(R_E²/g)
B.
T₀ = 2π√(R_E/g)
C.
T₀ = 2πR_E/g
D.
T₀ = √(2πR_E/g)
ANSWER :
B. T₀ = 2π√(R_E/g)
10.
The near-surface orbital period T₀ = 2π√(R_E/g) ≈ 85 minutes. This value can also be expressed as T₀ = 2π√(R_E³/GM_E). What is the physical significance of this minimum period?
A.
Satellites must orbit for at least 85 minutes to stay in orbit
B.
No artificial satellite can have a time period less than about 85 minutes while orbiting Earth
C.
The geostationary satellite has a period of 85 minutes
D.
The Earth completes one rotation in 85 minutes
ANSWER :
B. No artificial satellite can have a time period less than about 85 minutes while orbiting Earth
11.
A satellite orbits at radius r from Earth's centre. If the orbital radius is increased to 4r, the new time period is (original period = T):
A.
4T
B.
2T
C.
8T
D.
16T
ANSWER :
C. 8T
12.
The geostationary satellite has a time period of 24 hours and orbits at radius R_G from Earth's centre. A near-surface satellite has period T₀ ≈ 1.4 hours. The ratio R_G/R_E is approximately:
A.
(24/1.4)^(2/3) ≈ 6.6
B.
24/1.4 ≈ 17.1
C.
(24/1.4)^(1/2) ≈ 4.1
D.
(24/1.4)^2 ≈ 294
ANSWER :
A. (24/1.4)^(2/3) ≈ 6.6