A hollow cubical box is 0.822 m on an edge. This box is floating in a lake with
ID: 2144358 • Letter: A
Question
A hollow cubical box is 0.822 m on an edge. This box is floating in a lake with 1/2 of its height beneath the surface. The walls of the box have a negligible thickness. Water is poured into the box. What is the depth of the water in the box at the instant the box begins to sink?
A hollow cubical box is 0.822 m on an edge. This box is floating in a lake with 1/2 of its height beneath the surface. The walls of the box have a negligible thickness. Water is poured into the box. What is the depth of the water in the box at the instant the box begins to sink?Explanation / Answer
initially when the box is hollow :
Dw*g*h=m1*g where m1 is the mass of the hollow box and Dw is the density of water in the lake .
thus h = height below which the box is immersed .
h=0.822/2 = 0.411m
therefore m1= Dw*(0.411)
when water is filled in the box let mass of water be m2
m2=Dw*x*A where A= area of any surface of box and x= height upto which water is filled
A=0.811^2
when water is filled the force balance equation for hollow box becomes :
Dw*g*H= (Mh+Mw)*g where Mh is the mass of hollow box and Mw mass of water added
and H = length of box as box is immersed
therefore
Dw*(0.822)=(Dw*0.411+Dw*x*0.822^2)
thus we get x= 1/1.644 as the answer
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