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9-1.Fluid Mechanics
hard
A body of density $\rho'$ is dropped from rest at a height $h$ into a lake of density $\rho$ , where $\rho > \rho '$ . Neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface.
A
$\frac{h}{{\rho \,\, - \,\,\rho '}}$
B
$\frac{{h\,\rho '}}{\rho }$
C
$\frac{{h\,\rho '}}{{\rho \,\, - \,\,\rho '}}$
D
$\frac{{h\,\rho }}{{\rho \,\, - \,\,\rho '}}$
Solution
lets say it sinks to the depth $H$, at this instant final velocity becomes $v=0,$ so we have $0=(\sqrt{2 g h})^{2}-2 \times g\left(\frac{\rho-\rho'}{\rho}\right) \times H \quad \because v^{2}=u^{2}+2 a s$
$\Rightarrow H=\left(\frac{h \rho^{\prime}}{\rho-\rho'}\right)$
Standard 11
Physics
