0.1 percent of 1.728 × 106 spherical droplets of water, each of diameter 2 mm, coalesce to form a spherical bubble. What is the diameter (in cm) of the bubble?
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 2.4.
Volume of sphere = 4/3πr3
Radius of spherical droplets of water = 2/2 = 1 mm
Volume = 4/3π × 13 = 4/3π mm3
Hence, Volume of 0.1% of all spherical droplets
= 0.001 × 1.728 × 106 × 4/3π
= 4/3π × 1.728 × 103 mm3
Since spherical droplets coalesce to form a spherical bubble:
4/3π × 1.728 × 103 = 4/3π × R3
⇒ R3 = 1.728 × 103 mm3
⇒ R = 1.2 × 10 mm
⇒ R = 1.2 cm
Diameter = 2.4 cm