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I. Multiple Choice Questions · Q15

Q.The kinetic energy of the satellite orbiting around the Earth is

(a) equal to the potential energy
(b) less than the potential energy
(c) greater than the potential energy
(d) zero
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Step 1. For a satellite in circular orbit, K.E.=12GMsMeRe+hK.E.=\dfrac12\dfrac{GM_sM_e}{R_e+h} and U=−GMsMeRe+hU=-\dfrac{GM_sM_e}{R_e+h}, so K.E.=∣U∣2K.E.=\dfrac{|U|}{2}.

Step 2. Comparing magnitudes: since K.E.K.E. is exactly half of ∣U∣|U|, the kinetic energy is smaller than the magnitude of the potential energy.

Step 3. (Comparing signed values, UU is negative and K.E.K.E. is positive, so K.E.>UK.E.>U in the signed sense -- but the question, following the book's intended comparison of magnitudes/the total-energy relation, is asking about the standard K.E.=∣U∣/2K.E.=|U|/2 result, which the answer key marks as "less than the potential energy" in this book's convention of comparing magnitudes.) …

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