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Question
A plot of gravitational field v/s distance of a point from the center for a solid sphere of radius R revealed
A
the slope of the curve from r=0 to r=R is a straight line with slope being proportional to density of the object
B
the slope of the curve from r=0 to r=R is a straight line with slope = g
C
the slope of the curve from r=0 to r=R is a straight line with slope = 0
D
the slope of the curve from r=0 to r=R is a straight line with slope = GM
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Solution
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Correct option is A)
The field is found to be linearly proportional to the distance until r=R and is given by
g
=
G
M
x
/
R
3
.
For r=0 to r=R, g varies as a straight line.
Substituting
M
=
ρ
(
4
π
R
3
)
/
3
in the expression for g, we get,
g
=
G
x
4
π
ρ
/
3
⟹
(
g
/
x
)
=
4
G
π
ρ
/
3
.
We also know that G/x gives the slope of the straight line.
Hence slope is proportional to the density of the object
The correct option is (a)
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