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KVPY SX SB Exam 19-Nov-2017 Question Paper
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© examsnet.com
Question : 93
Total: 120
A uniform thin wooden plank AB of length L and mass M is kept on a table with its B end slightly outside the edge of the table. When an impulse J is given to the end B, the plank moves up with centre of mass rising a distance 'h' from the surface of the table. Then-
h
>
9
J
2
∕
8
M
2
g
h
=
J
2
∕
2
M
2
g
J
2
∕
2
M
2
g
<
h
<
9
J
2
∕
8
M
2
g
h
<
J
2
∕
2
M
2
g
Validate
Solution:
Case-IConsidering angular momentum w.r.t. end A
ω = Angular velocity just after impulse then
(
ω
)
(
M
L
2
3
)
=
J
(
L
)
ω
=
3
J
M
L
⇒ velocity of CM
V
c
m
1
=
ω
L
2
=
3
J
M
L
...(1)
Case-II
Apply conservation o moment, if 2
V
c
m
2
= Velocity of CM just after impulse
then
M
V
c
m
2
=
J
V
c
m
2
=
J
M
...(2)
comparing (1) & (2)
$V_{cm_2}
⇒ velocity of CM just after impulse would be between above two extreme values
with (1),
M
g
h
max
.
<
1
2
(
M
)
(
3
J
2
M
)
2
⇒
h
max
<
9
J
2
8
M
2
g
...(3)
M
g
h
max
.
<
1
2
(
M
)
(
J
M
)
2
h
max
<
J
2
2
M
2
g
...(4)
Use (3) & (4)
Hence
J
2
2
M
2
g
<
h
max
<
9
J
2
8
M
2
g
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