A small steel sphere is allowed to fall in a long vertical viscous liquid column. When the sphere has achieved 50% of its terminal velocity, its acceleration is [take g = 10 m/s2; ignore buoyant force]
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a
2.5 m/s2
b
5 m/s2
c
4 m/s2
d
8 m/s2
answer is B.
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Detailed Solution
At terminal velocity, mg=6πηrVTWhen V=VT2, viscous drag, FD=6πηrVT2, ∴ net force Fnet=mg−6πηrVT12=mg−mg×12=12mg∴ Acceleration =mg/2m=g2=5 m/s2