Density (D) is defined as the amount or mass (m) of a substance present in a unit volume(V). It can be expressed mathematically as:
Density = Mass/Volume
i.e. D = m/V -------(1)
Units: g/cm3
a)
If m1, V1 and D1 = mass, volume and density respectively of ball A
m2, V2 and D2 = mass, volume and density respectively of ball B
It is given that: V1 = V2; but m1 = 2m2
Based on equation (1) we have:
D1/D2 = (m1/V1)* (V2/m2) = (2m2/V2)*(V2/m2) = 2
Thus, density of ball A is twice that of B.
Ans: Ball A will have a greater density than B
b)
If m1, V1 and D1 = mass, volume and density respectively of ball C
m2, V2 and D2 = mass, volume and density respectively of ball D
It is given that:
V1 = 3V2 and m2 = 1/3(m1) i.e m1 = 3m2
Therefore,
D1/D2 = (m1/V1)* (V2/m2) = (3m2/3V2)*(V2/m2) = 1
Thus, D1 = D2
Ans: Their densities are equal
c)
If m1, V1 and D1 = mass, volume and density respectively of ball P
m2, V2 and D2 = mass, volume and density respectively of ball Q
It is given that:
m1 = m2 but V1 = 2V2
Therefore,
D1/D2 = (m1/V1)* (V2/m2) = (m2/2V2)*(V2/m2) = 1/2
Thus, D1 = 1/2(D2)
Ans: Ball Q will have a greater density.
d)
If m1, V1 and D1 = mass, volume and density respectively of ball X
m2, V2 and D2 = mass, volume and density respectively of ball Y
It is given that:
V1 = 2V2 and m1 = 1/2(m2)
Therefore,
D1/D2 = (m1/V1)* (V2/m2) = ((1/2(m2)/2V2)*(V2/m2) = 1/4
Thus, D1 = 1/4(D2)
Ans: Ball Y will have a greater density.
