A body of density ⍴' is dropped from rest at a height h into
a lake of density ⍴ where ⍴ > ⍴' neglecting all dissipative
forces, calculate the maximum depth to which the body sinks
before returning to float on the surface :
(a)h/⍴ - ⍴'
(b)h⍴'/⍴ (c)h⍴'/⍴ - ⍴'
(d)h⍴/⍴-⍴'
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Answer:
Velocity of the ball as it reaches water surface is
2gh
Net upward force acting on the body F=σVg−ρVg
⇒ma=σVg−ρVg
⇒(ρV)a=Vg(σ−ρ)
⇒a=g(
ρ
σ−ρ
) in upward direction
lets say it sinks to the depth H, at this instant final velocity becomes v=0, so we have
0=(
2gh
)
2
−2×g(
ρ
σ−ρ
)×H ∵v
2
=u
2
+2as
⇒H=(
σ−ρ
hρ
)
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