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JEE Main Physics Class 11 Laws Of Motion Part 1 Questions
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© examsnet.com
Question : 27
Total: 100
A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate
d
M
(
t
)
d
t
=
b
v
2
(
t
)
,
where
v
(
t
)
is its instantaneous velocity. The instantaneous acceleration of the satellite is :
[Sep. 05, 2020 (II)]
−
b
v
3
(
t
)
−
b
v
3
M
(
t
)
−
2
b
v
3
M
(
t
)
−
b
v
3
2
M
(
t
)
Validate
Solution:
From the Newton's second law,
F
=
d
p
d
t
=
d
(
m
v
)
d
t
=
v
(
d
m
d
t
)
......(i)
We have given,
d
M
(
t
)
d
t
=
b
v
2
(
t
)
.....(ii)
Thrust on the satellite,
F
=
−
v
(
d
m
d
t
)
=
−
v
(
b
v
2
)
=
−
b
v
3
[
Using (i) and (ii)
]
⇒
F
=
M
(
t
)
a
=
−
b
v
3
⇒
a
=
−
b
v
3
M
(
t
)
© examsnet.com
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