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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3sc154

A given mass of gold is dispersed first as spherical particles of radius and then as spherical particles of radius (same total mass, same density). Select the correct statements for the second sol compared with the first.

  1. AThe number of particles is one-eighth as large
  2. BThe total surface area of all the particles is half as large
  3. CThe surface area of a single particle is twice as large
  4. DThe mass of a single particle is eight times as large

Answer: A, B, D

Mass of one particle is proportional to , so doubling makes it 8 times larger and the number of particles for the same total mass one-eighth. Surface area of one particle is proportional to , so it becomes four times larger, not twice. Total area = number x area per particle = of the original.
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