Question

Questions based on Higher Order Thinking Skills:

There are three spheres A, B, C as shown below. Sphere A and B are made of same material. Sphere C is made of a different material. Spheres A and C have equal radii. The radius of sphere B is half that of A. Density of A is double that of C.

Now answer the following questions:

1. Find the ratio of masses of spheres A and B.
2. Find the ratio of volumes of spheres A and B.
3. Find the ratio of masses of spheres A and C.

Answer 1

i. Ratio of masses of spheres A and B:

M_A : M_B

D × V_A : D × V_B

Let the mass of sphere A = M_A

Let the mass of sphere B = M_B

Mass = Density × Volume

M_A = D_A × V_A

M_B = D_B × V_B  ...(Density is same)

Volume of Sphere A = `4/3πr^3`

Volume of sphere B = `4/3pi xx (("r"_"A")/2)^3`

`cancel("D") xx cancel(4/3) cancel(pi"r"^3) : cancel"D" xx cancel (4)/cancel(3) cancelpi (cancel("r")/2)^cancel(3)`

= `1 : 1/8`

= 8 : 1

ii. Ratio of volumes of spheres A and B:

V_A : V_B

8 : 1  ...(As mass is directly proportional to volume)

iii. Ratio of masses of spheres A and C:

M_A : M_C

`2cancel"D"xx cancel"V" : cancel"D"xx cancel"V"`

2 : 1  ...[∴ Density of A is double that of C]