Question

In case of earth
A. potential is minimum at the centre
B. potential is zero, both at centre and infinity
C. fields is zero both at centre and infinity
D. potential is same, both at centre and infinity but not zero

Answer 1

Correct Answer - A::B
Gravitational potential at a point inside the earth at a distance `r` from the centre of earth is,
`V = (-Gm(3R^(2) -r^(2)))/(2R^(3))`
At the centre of earth, `r = 0`,
`V = - (GM)/(2R^(3)) xx (3R^(2) - 0) = - (3GM)/(2R)` (Minimum)
For a point outside the earth at distance `r` from
centre of earth, `V = - (GM)/(r )`
When `r = oo, V = - (GM)/(oo) = 0`
Gravitational intensity at a point distance `r` from
the centre of earth is `I = (GM)/(r^(2))`,
When `r = oo, I = 0`
When point is inside the earth, then
`I = (G)/(r^(2)) xx (4)/(3) pi r^(3) rho` or `I = (4piG rho r)/(3)`
When `r = 0, I = 0`