One end of a uniform stick having length l=1m is hung from a string as shown in figure. Length a=20 cm is above the point of suspension the length of the stick below the surface of water is `[rho_("stick")//rho_("liquid")=0.25]`

Options

A. x=0.1m
B. x=0.15m
C. x=0.2m
D. x=0.25m

Answer

A

Explanation

`tau_("net")=0` [about point of suspension]
`F_(B)(l-a-(x)/(2))cosalpha=w((l)/(2)-a)cosalpha`
Putting `F_(B)=Axrho_(l)` & `W=Alrho_(S)`
`x=(l-a)+-sqrt((l-a)^(2)-(rho_(l))/(rho_(0))l(l-2a))=0.1`m
Since xlt(l-a), discard + sign in te solution.