A cubical block of wood having mass of 160 ~g has a metal piece fastened underneath as shown in the figure. Find the maximum mass of the metal piece which will allow the block to float in water. Specific gravity of wood is 0.8 and that metal is 10 and density of water =1 ~g / cc .

Step-by-step solution

Volume of wood block = Mass Density = 160 0.8 1 = 1600 8 =200 ~cm ^3 Let mass of metal piece is x ~g . Volume of metal piece = Mass Density = x 10 1 = x 10 ~cm ^3 Total volume of fluid displaced = (200+ x 10 ) 10⁻⁶ ~m ^3 Weight of fluid displaced =V _f g= (200+ x 10 ) 10⁻⁶ 1000 10= (200+ x 10 ) 10⁻² ~N If block floats in water, then weight = upthrust (160+x) 10 10⁻³= (200+ x 10 ) 10⁻²160+x=200+ x 10 9 x 10 =40x= 400 9 =44.4 ~g