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MHT CET 2020 Physics Solved Paper
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© examsnet.com
Question : 47
Total: 50
A U-tube is of non uniform cross-section. The area of cross-sections of two sides of tube are
A
and
2
A
(see fig.). It contains non-viscous liquid of mass
m
. The liquid is displaced slightly and free to oscillate. Its time period of oscillations is
T
=
2
π
√
m
3
ρ
g
A
T
=
2
π
√
m
2
ρ
g
A
T
=
2
π
√
m
ρ
g
A
None of these
Validate
Solution:
Suppose the liquid in left side limb is displaced slightly by
y
, the liquid in right limb will increase by
y
∕
2
. The restoring force
F
=
−
P
A
=
−
ρ
g
(
3
y
2
)
×
2
A
=
3
ρ
g
A
(
−
y
)
.
a
=
F
m
=
3
ρ
g
A
(
−
y
)
∕
m
On comparing with,
a
=
−
ω
2
y
, we get
ω
=
√
3
ρ
g
A
m
and
T
=
2
π
√
m
3
ρ
g
A
© examsnet.com
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