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Physics
Physics
Problem
The mass density of a planet of radius
R
R
R
varies with the distance
r
r
r
from its centre as
ρ
(
r
)
=
ρ
0
(
1
−
r
2
R
2
)
\rho(r) = \rho_0 \left(1 - \frac{r^2}{R^2}\right)
ρ
(
r
)
=
ρ
0
(
1
−
R
2
r
2
)
. Then, the gravitational field is maximum at (a)
r
=
3
4
R
r = \sqrt{\frac{3}{4}} R
r
=
4
3
R
(b)
r
=
R
r = R
r
=
R
(c)
r
=
5
9
R
r = \sqrt{\frac{5}{9}} R
r
=
9
5
R
(d)
r
=
1
3
R
r = \frac{1}{\sqrt{3}} R
r
=
3
1
R
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