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JEE Main Physics Class 11 Gravitation Part 1 Questions
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© examsnet.com
Question : 64
Total: 100
Figure shows elliptical path abed of a planet around the sun S such that the area of triangle csa is
1
4
the area of the ellipse. (See figure) With db as the semimajor axis, and ca as the semiminor axis. If
t
1
is the time taken for planet to go over path abs and
t
2
for path taken over cda then:
[Online April 9, 2016]
t
1
=
4
t
2
t
1
=
2
t
2
t
1
=
3
t
2
t
1
=
t
2
Validate
Solution:
Let area of ellipse abcd =x
Area of
S
a
b
c
S
=
x
2
+
x
4
(i.e., ar of abca
+
S
a
c
S
)
(Area of half ellipse + Area of triangle)
=
3
x
4
Area of
S
a
d
c
S
=
x
−
3
x
4
=
x
4
Area of
S
a
b
c
S
Area of
S
a
d
c
S
=
3
x
∕
4
x
∕
4
=
t
1
t
2
t
1
t
2
=
3
or,
t
1
=
3
t
2
© examsnet.com
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