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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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