A silt is cut at the bottom, along the right bottom edge of a rectangular tank. The slit is closed by a wooden wedge of mass `m` and apex angle `theta` as shown in figure. The vertical plane surface of the wedge is in contact with the right vertical wall of the container. coefficient of static friction between these two surfaces is `mu`. To what maximum height can water be filled in the tank without leakage from the slit ? The width of tank is b and density of water is `rho`.

Options

A. `sqrt((2m)/(rhob(tantheta-mu)))`
B. `sqrt((4m)/(rhob(tantheta-mu)))`
C. `sqrt((2m)/(rhob(sintheta-mucostheta)))`
D. `sqrt((2mcostheta)/(rhob(tantheta-mucostheta)))`

Answer

A

Explanation

`mg+muN=F_("pressure")`
`impliesmg+mu[rhog.(h)/(2)(bh)]=rhog[(1)/(2)xxhtanthetaxxh]`
`impliesmg+(murhogh^(2)b)/(2)=(rhogh^(2)tantheta)/(2)`
`impliesm=(bh^(2)rho)/(2)[tantheta-mu]becauseh=sqrt((2m)/((tantheta-mu)brho))`