A cylinder is filled with a liquid of refractive index `mu`. The radius of the cylinder is decreasing at a constant rate `K`. The volume of the liquid inside the container remains constant at `V`. The observer and the object `O` are in a state of rest at a distance `L` from each other. When radius of cylinder is `r` the apparent velocity of the object as seen by the observer is

Options

A. `((1-mu)2KV)/((pimur^(3)))`
B. `((1-mu)2KV)/((pimulr^(2)))`
C. `((1-mu)2K)/(mu)`
D. `((1-mu)K)/(2mu)`

Answer

A

Explanation

`X_("app") =L-H+H/(mu)`
`(dX_("app"))/(dt)=(dH)/(dt) ((1-mu)/(mu))`
`pi r^(2)H=V`
`:.(dH)/(dt)=-(2H)/r (dr)/(dt)+(2KH)/r`
`:. (dX_("app"))/(dt)=(2KV)/(pir^(3))(((1-mu))/(mu))`