Q.

Eight identical droplets of water were falling in air with constant velocity 2cm/s. The initial acceleration of each droplet was 'a1'  at the time when they start falling. At a time  't', these droplets coalesce to form a big drop due to pressure difference developed and just after the formation of combined drop, its acceleration is found  'a2'. The ratio of 3a1a2  is

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answer is 4.

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Detailed Solution

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m1a1=6πηr1v1

m2a2=6πηr2(v2v1)

a1a2=r1v1m2r2(v2v1)m1=43

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Eight identical droplets of water were falling in air with constant velocity 2 cm/s. The initial acceleration of each droplet was 'a1'  at the time when they start falling. At a time  't', these droplets coalesce to form a big drop due to pressure difference developed and just after the formation of combined drop, its acceleration is found  'a2'. The ratio of 3a1a2  is