Physics
Mechanics
Easy

Question

Let V and E denote the gravitational potential and gravitational field, respectively, at a point due to certain uniform mass distribution described in four different situations of Column I. Assume the gravitational potential at infinity to be zero. The values of E and V are given in Column II Match the statement in column I with the results in Column II.

Column I

Column II

i. At the centre of thin spherical shell
a. E = 0
ii. At the centre of solid sphere
b. E ≠ 0
iii. A solid sphere has a non-concentric spherical cavity. At the centre of the spherical cavity
c.  V ≠ 0
iv. At the centre of the joining two point masses of equal magnitude
d.  V = 0

  1. text  i.  end text rightwards arrow text  a.c; ii.  end text rightwards arrow text  a.c; iii.  end text rightwards arrow text  a.c; iv.  end text rightwards arrow text  a.c  end text
  2. text  i.  end text rightwards arrow b comma c semicolon i i. rightwards arrow a comma c semicolon text  iii.  end text rightwards arrow a comma c semicolon i v times rightwards arrow a comma c
  3. text  i.  end text rightwards arrow text  b.c; ii.  end text rightwards arrow text  b.c; iii.  end text rightwards arrow text  a.c; iv.  end text rightwards arrow text  a.c  end text
  4. rightwards arrow text  ca; ii.  end text rightwards arrow text  a.c; iii.  end text rightwards arrow text  a, b; iv.  end text rightwards arrow text  a.c  end text

The correct answer is: text  i.  end text rightwards arrow text  a.c; ii.  end text rightwards arrow text  a.c; iii.  end text rightwards arrow text  a.c; iv.  end text rightwards arrow text  a.c  end text


    i. At centre of thin spherical shell, .V not equal to 0 comma E equals 0
    ii. At centre of solid sphere, V not equal to 0 comma E equals 0.
    iii. At centre of spherical cavity inside solid sphere, V not equal to 0 comma E not equal to 0
    iv. At centre of two point masses. V not equal to 0 comma E equals 0

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