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Putnam
Putnam 1938
A7
A7
Part of
Putnam 1938
Problems
(1)
Putnam 1938 A7
Source:
8/20/2021
Do either
(
1
)
(1)
(
1
)
or
(
2
)
(2)
(
2
)
(
1
)
(1)
(
1
)
S
S
S
is a thin spherical shell of constant thickness and density with total mass
M
M
M
and center
O
.
O.
O
.
P
P
P
is a point outside
S
.
S.
S
.
Prove that the gravitational attraction of
S
S
S
at
P
P
P
is the same as the gravitational attraction of a point mass
M
M
M
at
O
.
O.
O
.
(
2
)
(2)
(
2
)
K
K
K
is the surface
z
=
x
y
z = xy
z
=
x
y
in Euclidean
3
ā
3-
3
ā
space. Find all straight lines lying in
S
S
S
. Draw a diagram to illustrate them.
Putnam