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. 1. `(hrho)/(sigma-rho)`
B. 2. `(h sigma)/(sigma-rho)`
C. 3. `(h rho)/(sigma)`
D. 4. `(h sigma)/(rho)`

Answer

A

Explanation

Velocity of body just before touching the lake surface is,
`v=sqrt(2gh)`
Retardation in the lake ,
`a=("upthrust-weight")/("mass")`
`=(V rhog-V rhog)/(Vrho) =((sigma-rho)/(rho))g`
Maximum depth `d_(max)=(v_2)/(2a)=(h rho)/(sigma-rho)` .