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AIIMS 201827 May
Exam
AIIMS
Year
2018
Date
27 May
Subject
Physics
Chapter
Gravitation

AIIMS 2018 · 27 May · Physics · Gravitation

Average distance of the earth from the sun is L_1 . If one year of...

Average distance of the earth from the sun is L1L_1. If one year of the earth =D=D days, one year of another planet whose average distance from the sun is L2L_2 will be

Options

  1. AD(L2L1)1/2D\left(\frac{L_2}{L_1}\right)^{1 / 2} days
  2. BD(L2L1)3/2D\left(\frac{L_2}{L_1}\right)^{3 / 2} days
  3. CD(L2L1)2/3D\left(\frac{L_2}{L_1}\right)^{2 / 3} days
  4. DD(L2L1)D\left(\frac{L_2}{L_1}\right) days

Correct answer

B. D(L2L1)3/2D\left(\frac{L_2}{L_1}\right)^{3 / 2} days

Step-by-step solution

According to Kepler's third law, T2∝r3T^2 \propto r^3 or T∝r3/2T \propto r^{3 / 2} ∴D′D=(L2L1)3/2\therefore \quad \frac{D^{\prime}}{D}=\left(\frac{L_2}{L_1}\right)^{3 / 2} \quad or D′=D(L2L1)3/2D^{\prime}=D\left(\frac{L_2}{L_1}\right)^{3 / 2} days
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