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JEE Main 201511 AprilOnline
Exam
JEE Main
Year
2015
Date
11 April
Mode
Online
Subject
Physics
Chapter
Gravitation

JEE Main 2015 · 11 April · Online · Physics · Gravitation

Which of the following most closely depicts the correct variation...

Which of the following most closely depicts the correct variation of the gravitation potential, V(r)V ( r ) with distance rr due to a large planet of radius RR and uniform mass density? (figures are not drawn to scale)Which of the following most closely depicts the correct variation of the gravitation potential, V ( r ) with distance rWhich of the following most closely depicts the correct variation of the gravitation potential, V ( r ) with distance rWhich of the following most closely depicts the correct variation of the gravitation potential, V ( r ) with distance rWhich of the following most closely depicts the correct variation of the gravitation potential, V ( r ) with distance r

Options

  1. AWhen 100 ~g of a liquid A at 100^ ^ ^ C is added to 50 ~g of a liquid B at temperature 75^ ^ ^ C , the temperature of
  2. BWhen 100 ~g of a liquid A at 100^ ^ ^ C is added to 50 ~g of a liquid B at temperature 75^ ^ ^ C , the temperature of
  3. CWhen 100 ~g of a liquid A at 100^ ^ ^ C is added to 50 ~g of a liquid B at temperature 75^ ^ ^ C , the temperature of
  4. DWhen 100 ~g of a liquid A at 100^ ^ ^ C is added to 50 ~g of a liquid B at temperature 75^ ^ ^ C , the temperature of

Correct answer

C. When 100 ~g of a liquid A at 100^ ^ ^ C is added to 50 ~g of a liquid B at temperature 75^ ^ ^ C , the temperature of

Step-by-step solution

At inside points (r<R)( r < R ), V=−GM2R3(3R2−r2).SoatV = - \dfrac{GM}{2{R}^{3}}\left(3{R}^{2} - {r}^{2}\right). So at the centre,r = 0 ⇒ V = - 32GMR.Atoutsidepoints(r>R),\dfrac{3}{2}\dfrac{GM}{R}. At outside points \left(r > R\right),V = −GMr.Atsurface,\dfrac{- GM}{r}. At surface,V = −GMR.So\dfrac{- GM}{R}. So the gravitational potential is non-uniform and negative.
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