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NEET 2018
Exam
NEET
Year
2018
Subject
Physics
Chapter
Gravitation

NEET 2018 · Physics · Gravitation

The kinetic energies of a planet in an elliptical orbit about the...

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions, A,BA, B and CC are KA,KBandKC{K}_{A}, {K}_{B}and{K}_{C}, respectively. ACAC is the major axis and SBSB is perpendicular to ACAC at the position of the Sun SS as shows in the figure. Then

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions, A, B and C are K _ A , K _ B and K

Options

  1. AKB<KA<KC{K}_{B} < {K}_{A} < {K}_{C}
  2. BKA>KB>KC{K}_{A} > {K}_{B} > {K}_{C}
  3. CKA<KB<KC{K}_{A} < {K}_{B} < {K}_{C}
  4. DKB>KA>KC{K}_{B} > {K}_{A} > {K}_{C}

Correct answer

B. KA>KB>KC{K}_{A} > {K}_{B} > {K}_{C}

Step-by-step solution

By angular momentum consentration about the sun,
L=Iω=L = I\omega = constant
KE=L22IKE = \dfrac{{L}^{2}}{2I}
∵SA∠SB∠SC∵ SA ∠ SB ∠ SC
⇒⇒ IA<IB<IC{I}_{A} < {I}_{B} < {I}_{C}
KEA>KEB>KEC{KE}_{A} > {KE}_{B} > {KE}_{C}
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