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In case of earth...

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

Text Solution

Verified by Experts

The correct Answer is:
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`
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