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प्रश्न
Questions based on Higher Order Thinking Skills:
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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.
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Now answer the following questions:
- Find the ratio of masses of spheres A and B.
- Find the ratio of volumes of spheres A and B.
- Find the ratio of masses of spheres A and C.
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उत्तर
i. Ratio of masses of spheres A and B:
MA : MB
D × VA : D × VB
Let the mass of sphere A = MA
Let the mass of sphere B = MB
Mass = Density × Volume
MA = DA × VA
MB = DB × VB ...(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:
VA : VB
8 : 1 ...(As mass is directly proportional to volume)
iii. Ratio of masses of spheres A and C:
MA : MC
`2cancel"D"xx cancel"V" : cancel"D"xx cancel"V"`
2 : 1 ...[∴ Density of A is double that of C]
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