consider 3 spheres, sphere 1 and sphere 2 are made up of same material and sphere 3 is different and sphere 1 and sphere 3 are having same radius and sphere 2 is half the radius of sphere 1 and density of sphere 1 is double that of sphere 3. Calculate i) ratio of masses and volumes of sphere1 and sphere2.
ii) ratio of masses of sphere1 and sphere3
Answers
there are three spheres ; 1 , 2 and 3
a/c to question, sphere 1 and sphere 2 are made up of same material.
so, density of sphere 1 = density of sphere 2 = d
density of sphere 1 = 2 × density of sphere 3
so, density of sphere 3 = d/2
sphere 1 and sphere 3 are having same radius. e.g., radius of sphere 1 = radius of sphere 3 = r
and radius of sphere 2 = r/2
(i) so, mass of sphere 1 = density of sphere 1 × volume of sphere 1
= d × (4/3 πr³) = (4/3 πr³d)
mass of sphere 2 = density of sphere 2 × volume of sphere 2
= d × {4/3 π(r/2)³} = (1/8)(4/3πr³d)
mass of sphere 3 = density of sphere 3 × volume of sphere 3
= (d/2) × (4/3πr³) = (1/2)(4/3πr³d)
so, ratio of masses of sphere 1 and sphere 2 = 1 : 1/8
= 8 : 1
ratio of volume of sphere 1 and sphere 2 = 1 : 1/8 = 8 : 1
(ii) ratio of masses of sphere 1 and sphere 3 = 1 : 1/2 = 2 : 1
Answer:
there are three spheres ; 1 , 2 and 3
a/c to question, sphere 1 and sphere 2 are made up of same material.
so, density of sphere 1 = density of sphere 2 = d
density of sphere 1 = 2 × density of sphere 3
so, density of sphere 3 = d/2
sphere 1 and sphere 3 are having same radius. e.g., radius of sphere 1 = radius of sphere 3 = r
and radius of sphere 2 = r/2
(i) so, mass of sphere 1 = density of sphere 1 × volume of sphere 1
= d × (4/3 πr³) = (4/3 πr³d)
mass of sphere 2 = density of sphere 2 × volume of sphere 2
= d × {4/3 π(r/2)³} = (1/8)(4/3πr³d)
mass of sphere 3 = density of sphere 3 × volume of sphere 3
= (d/2) × (4/3πr³) = (1/2)(4/3πr³d)
so, ratio of masses of sphere 1 and sphere 2 = 1 : 1/8
= 8 : 1
ratio of volume of sphere 1 and sphere 2 = 1 : 1/8 = 8 : 1
(ii) ratio of masses of sphere 1 and sphere 3 = 1 : 1/2 = 2 : 1