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BITSAT 2020 Solved Question Paper
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© examsnet.com
Question : 4
Total: 150
A body of density
ρ
′
is dropped from rest at a height
h
into a lake of density
ρ
where
ρ
>
ρ
′
neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface :
h
ρ
−
ρ
′
h
ρ
′
ρ
h
ρ
′
ρ
−
ρ
′
h
ρ
ρ
−
ρ
′
Validate
Solution:
Velocity of the ball as it reaches water surface is
√
2
g
h
Net upward force acting on the body
F
=
ρ
V
g
−
ρ
′
V
g
⇒
m
a
=
ρ
V
g
−
ρ
′
V
g
⇒
(
ρ
′
V
)
a
=
V
g
(
ρ
−
ρ
′
)
⇒
a
=
g
(
ρ
−
ρ
′
ρ
′
)
in upward direction
lets say it sinks to the depth
H
, at this instant final velocity becomes
v
=
0
, so we have
0
=
(
√
2
g
h
)
2
−
2
×
g
(
ρ
−
ρ
′
ρ
′
)
×
H
∵
v
2
=
u
2
+
2
as
⇒
H
=
(
h
ρ
′
ρ
−
ρ
′
)
© examsnet.com
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