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KVPY 2020-21 SA Exam Previous Papers
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© examsnet.com
Question : 19
Total: 80
A spacecraft which is moving with a speed u relative to the earth in the x-direction, enters the gravitational field of a much more massive planet which is moving with a speed 3u in the negative x-direction. The spacecraft exists following the trajectory as shown below.
The speed of the spacecraft with respect to the earth a long a time after it has escaped the planet’s gravity is given by
u
4u
2u
7u
Validate
Solution:
From conservation of angular momentum
m
v
1
r
=
m
v
2
r
Initial velocity of spacecraft w.r.t. planet
(
→
v
s
∕
p
)
initial
=
4
u
Final velocity of the spacecraft w.r.t. planet
(
→
v
s
∕
p
)
final
=
−
4
u
Now,
→
v
S
∕
E
=
→
v
S
∕
P
−
→
v
E
∕
P
= –4u – (3u) = – 7u
Hence, speed of spacecraft w.r.t. earth finally becomes 7u
© examsnet.com
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