NEETPhysicsMechanical Properties of Fluids
A tiny spherical glass bead is projected vertically downwards into a deep column of highly viscous oil. Its initial downward velocity v₀ is twice its terminal velocity ( v₀ = 2v_t ). Which of the following descriptions correctly shows the variation of its velocity ( v ) with time ( t )?
Options
- AA curve starting at v₀ on the velocity axis and decreasing with a continuously flattening slope to approach a
- BA curve starting at v₀ on the velocity axis and decreasing continuously to approach zero asymptotically.
- CA straight line starting at v₀ on the velocity axis and decreasing linearly until it abruptly becomes horizont
- DA curve starting at v₀ on the velocity axis and increasing with a continuously flattening slope to approach a
Correct answer
A. A curve starting at v₀ on the velocity axis and decreasing with a continuously flattening slope to approach a
Step-by-step solution
The net downward force on the spherical bead is given by F_ net = W_ eff - F_v , where W_ eff is the effective weight (weight minus buoyancy) and F_v is the velocity-dependent viscous drag. At terminal velocity v_t , the net force is zero, so W_ eff = 6 r v_t . The bead is projected with an initial velocity v₀ = 2v_t . Since v₀ > v_t , the initial upward viscous drag is greater than the downward effective weight. This results in a net upward force, causing the bead to decelerate. As the velocity decreases, the visc