A body of density `rho` is dropped from a height h into a lake of density `sigma(sigmagtrho)`. The maximum depth the body sinks inside the liquid is (neglect viscous effect of liquid)

Options

A. `(h rho)/(sigma-rho)`
B. `(h sigma)/(sigma-rho)`
C. `(hrho)/(sigma)`
D. `(hsigma)/(rho)`

Answer

A

Explanation

`v=sqrt(2gh)`
Retardation in liquid `a=(V sigma g-V rho g)/(V)=((sigma-rho)/(rho))g`
`therefore " " d_("max")=(v^(2))/(2a)=(2gh)/(2xx((sigma-rho)/(rho))g)=(rho h)/(sigma-rho)`