Please show your work! The answer is C. What is the approximate minimum area of

Question

Please show your work!

The answer is C.

What is the approximate minimum area of the top surface of a rectangular slab of ice 0.3 m thick floating on fresh water that will hold an automobile of mass 1100 kg just above the surface of the water? Assume the centers of mass of the car and die ice are vertically aligned. Take the densities of water and ice to be 998 kg/m^3 and 917 kg/m^3, respectively. A. 3.7m^2 B. 444m^2 C. 46m^2 D. no area is large enough E. area cannot be determined from the information given

Explanation / Answer

Let A is the surface area of reactangular slab.

volume of slab, V = A*d

= A*0.3 m^3

In the equilibrium,

Buoyant force = weight of the ice slab + weight of automobile

weight of the water displaced = weight of the ice slab + weight of automobile

V*rho_water*g = V*rho_ice*g + m*g

V*rho_water = V*rho_ice + m

A*0.3*998 = A*0.3*917 + 1100

A*(0.3*998 - 0.3*917) = 1100

A = 1100/(0.3*998 - 0.3*917)

= 45.27 m^2

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