A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph show

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Question

A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball (v) as a function of time (t) is
[Note: The graph shows four curves labeled A, B, C, D. Curve A rises linearly, Curve B rises and gradually flattens to a constant terminal value, Curve C is a horizontal straight line, and Curve D decreases with time.]

Accepted Answer

Correct Answer: C - Curve BStep-by-step Solution:When a ball is dropped in a viscous liquid, initially the gravitational force exceeds the viscous drag, so the ball accelerates. As speed increases, the viscous drag (F = 6πηrv) increases until it equals the net downward force (weight minus buoyancy). At this point, acceleration becomes zero and the ball moves at a constant terminal velocity. The speed-time graph therefore rises and asymptotically approaches a constant value - this is represented by Curve B.Why other options are incorrect: Curve A (linear rise) would imply constant acceleration, ignoring viscous drag. Curve C (horizontal) would mean constant speed from the very start. Curve D (decreasing) has no physical basis for a falling body.Key Concept: Terminal velocity is reached when viscous drag + buoyancy = weight. v_terminal = 2r²(ρ - σ)g / 9η, where ρ is ball density, σ is liquid density, and η is the coefficient of viscosity.

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