The correct option is C 5×(4)1/3 cm/s
Terminal velocity for a spherical body of radius R and density ρ falling in a liquid of density σ and dynamic viscosity η is given by,
VT=29(ρ−σ)R2gη
⇒VT∝R2
Let two identical drops of radius R1 coalesce to form bigger drop of radius R2,
VT2VT1=R22R21(1)
Since the volume remains same before and after the drops coalesce. Therefore,
Vi=Vf
2×43πR31=43πR32
⇒R2=(2)1/3R1
Substituting this in equation (1),
VT2VT1=(4)1/3R21R21
VT2=5×(4)1/3 cm/s