Eight identical drops of water falling through air with uniform velocity of 10cm/s combine to form a single drop of big size, then terminal velocity…

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Eight identical drops of water falling through air with uniform velocity of 10cm/s combine to form a single drop of big size, then terminal velocity of the big drop will be

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Correct answer: (D) 40 cm/s. Given, terminal velocity of each small drop v_1=10cm/s When 8 small drops are combined to form bigger If r_1 be radius of small drop and r_2 be radius of bigger drop, then v_2=v_1 4/3πr23=8×4/3πr13⇒r_2=2r_1 ∴ Terminal velocity of the drop v=(2r^2)/9(p-σ)/(9η) i.e., v∝r^2 ∴v_1/v_2=r/12r22=r/(122r^12)⇒v_1/v_2=1/4 v_2=4v_2=4×10=40

Eight identical drops of water falling through air with uniform velocity of 10cm/s combine to form a single drop of big size, then terminal velocity of the big drop will be

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