Two loads, one made of wood (R) and another made of metal (r), tied together, ha

Question

Two loads, one made of wood (R) and another made of metal (r), tied together, hang motionlessly under water. How many times the wooden load is bigger than the metal one, if the density of metal is D_M = 14.5, and the density of wood is D_W = 0.5? Present answer as the ratio of the diameters R/r. The volume of a ball is V = (4/3) middot pi middot R^3. 1 kg of water at 50 degree C is mixed with 1 kg of acetone at 20 degree C. What is the temperature of the mix? The specific heat of acetone is C_ac = 0.50 kcal/kg degree C. There is 1kg of ice (0 degree C) in a thermos. How much boiling water (100 degree C) should be added into thermos in order to melt all ice? The latent heat of ice fusion q_ice is 80 cal/g. What is the density D of oil in a tube?

Explanation / Answer

Q1.

for the two loads to remain sub-merged, total weight should be equal to total buyoant force

==>volume of wooden sphere*density of wood+volume of metal sphere*density of metal=total volume of two spheres*density of water

==>(4/3)*pi*R^3*0.5+(4/3)*pi*r^3*14.5=(4/3)*pi*(R^3+r^3)*1

==>0.5*R^3+14.5*r^3=R^3+r^3

==>13.5*r^3=0.5*R^3

==>R=3*r

hence R/r=3

Question 2:

let temperature of the mix is T degree celcius.

then heat lost by water=heat gained by acetone

==>mass of water*specific heat of water*temperature difference=mass of acetone*temperature difference *specific heat of acetone

==>1*1*(50-T)=1*0.5*(T-20)

==>2*(50-T)=T-20

==>100-2*T=T-20

==>3*T=120

==>T=40 degree celcius

so temperature of the mix is 40 degree celcius

question 3:

let mass of water required is m grams.
total heat required to melt all ice=total heat lost by boiling water while bringing temperature down from 100 degree celcius to 0 degree celcius

==>1000*80 cal=m*1*(100-0)

==>m=800 grams

so 800 grams of boiling water is required

question 4:

8 cm of water gauge pressure=10 cm of oil gauge pressure

==>density of water*g*height=density of oil*g*height

==>1000*0.02=D*0.1

==>D=200 kg/m^3

so density of the oil is 200 kg/m^3.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.