An alloy is made of a material of specific gravity 7.87 and another material of specific gravity 4.50. The alloy of mass 750g has an apparent weight of 6.6N when totally immersed in a liquid of specific gravity 0.78. calculate the ratio of the volumes of the constituents of the alloy

13.9

Explanation:

Apparent weight is the normal force. Sum of the forces on the alloy when it is submerged:

∑F = ma

N + B - W = 0

N + ρVg - mg = 0

6.6 + (0.78 * 1000) V (9.8) - (0.750) (9.8) = 0

V = 9.81*10⁻⁵

If x is the volume of the first material, and y is the volume of the second material, then:

x + y = 9.81*10⁻⁵

(7.87*1000) x + (4.50*1000) y = 0.750

Two equations, two variables. Solve with substitution:

7870 (9.81*10⁻⁵ - y) + 4500 y = 0.750

0.772 - 7870 y + 4500 y = 0.750

0.0222 = 3370 y

y = 6.58*10⁻⁶

x = 9.15*10⁻⁵

The ratio of the volumes is:

x/y = 13.9