A small metal sphere is falling through a viscous liquid. The variation of velocity ( V ) with time ( t ) is shown correctly in graph

Step-by-step solution

When a small metal sphere falls through a viscous liquid, the forces acting on it are its weight ( W ) downwards, buoyant force ( F_B ) upwards, and viscous drag force ( F_v ) upwards. The equation of motion is given by: m dv dt = W - F_B - F_v m dv dt = mg - 4 3 r^3 g - 6 r v Initially at t=0 , v=0 , so the acceleration is maximum. As velocity increases, the viscous drag force ( 6 r v ) increases, which decreases the net force and hence the acceleration. Eventually, the net force becomes zero, and the sphere attai