Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A satellite is moving in a circular orbit of radius R around the earth. Which of the following
statements is incorrect?
Text Solution
Verified by ExpertsThe correct answer is:
C
Step 1: For a satellite in circular orbit, the angular momentum (L) is given by the formula:
L = mvr, where v is the linear velocity and r is the radius (R).
Since v is constant for a satellite in a stable orbit, L varies as R.
Therefore, angular momentum varies as R (Option A is correct).
Step 2: The linear momentum (p) of the satellite is given by p = mv. The linear velocity v is constant for a fixed radius R. Thus, p remains constant, and the statement is incorrect (Option B is correct).
Step 3: The kinetic energy (KE) of the satellite is given by KE = \frac{1}{2} mv^2. The velocity v can be derived as v = \sqrt{\frac{GM}{R}}. Thus, KE varies with R as \frac{1}{R} (Option C is incorrect, as stated).
Step 4: The frequency (f) of the orbiting satellite is determined by the orbital period (T), where T = 2\pi\sqrt{\frac{R^3}{GM}}, which shows that frequency varies as \frac{1}{R^{3/2}} (Option D is correct).
Therefore, the incorrect statement is about kinetic energy.
L = mvr, where v is the linear velocity and r is the radius (R).
Since v is constant for a satellite in a stable orbit, L varies as R.
Therefore, angular momentum varies as R (Option A is correct).
Step 2: The linear momentum (p) of the satellite is given by p = mv. The linear velocity v is constant for a fixed radius R. Thus, p remains constant, and the statement is incorrect (Option B is correct).
Step 3: The kinetic energy (KE) of the satellite is given by KE = \frac{1}{2} mv^2. The velocity v can be derived as v = \sqrt{\frac{GM}{R}}. Thus, KE varies with R as \frac{1}{R} (Option C is incorrect, as stated).
Step 4: The frequency (f) of the orbiting satellite is determined by the orbital period (T), where T = 2\pi\sqrt{\frac{R^3}{GM}}, which shows that frequency varies as \frac{1}{R^{3/2}} (Option D is correct).
Therefore, the incorrect statement is about kinetic energy.
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