Eight equal drops of water each of radius r = 2 mm are falling through air with the terminal velocity of 16 cm/s. The eight drops combine to form a big drop. The terminal velocity of the big drop is 16 × N cm/s. Find N.
Physics · Mixed Chapter
JEE Mains

Question

Eight equal drops of water each of radius r = 2 mm are falling through air with the terminal velocity of 16 cm/s. The eight drops combine to form a big drop. The terminal velocity of the big drop is 16 × N cm/s. Find N.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Volume conservation gives R³=8r³, so the larger radius is R=2r. Step 2: Under Stokes’ law the terminal speed of a small spherical drop is vₜ∝r². Step 3: Hence v_new/v_old=(R/r)²=4; v_new=64 cm/s=16×4 cm/s. Step 4: N=4.