Terminal Velocity NEET Questions

Physics - Properties of Solids and Liquids

Terminal Velocity MCQ Questions


7.
Why does a falling body reach a terminal velocity and not continue to accelerate indefinitely?
A.
Buoyancy increases indefinitely with depth
B.
Air has infinite density
C.
Gravity decreases with depth in a fluid
D.
Stokes drag force increases with velocity, eventually equalling the net gravitational force and making the net force zero
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ANSWER :
D. Stokes drag force increases with velocity, eventually equalling the net gravitational force and making the net force zero
8.
The formula for terminal velocity v_t of a sphere of radius a, density ρ, falling through a fluid of density σ and viscosity η is derived by equating weight to buoyancy plus Stokes drag. The result is:
A.
v_t = 2a²(ρ−σ)g / (3η)
B.
v_t = 2a²(ρ−σ)g / (9η)
C.
v_t = a²(ρ−σ)g / (9η)
D.
v_t = 4a²(ρ−σ)g / (9η)
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ANSWER :
B. v_t = 2a²(ρ−σ)g / (9η)
9.
In the derivation of terminal velocity, the step (4/3)πa³(ρ−σ)g = 6πηav_t gives v_t by dividing both sides by 6πηa. The intermediate simplification is:
A.
v_t = (4/3)πa²(ρ−σ)g / (6πη)
B.
v_t = a(ρ−σ)g / (9η)
C.
v_t = 4a²(ρ−σ)g / (3η)
D.
v_t = (4/3)πa³(ρ−σ)g / (6πηa) = 2a²(ρ−σ)g / (9η)
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ANSWER :
D. v_t = (4/3)πa³(ρ−σ)g / (6πηa) = 2a²(ρ−σ)g / (9η)
10.
The expression (ρ − σ) in the terminal velocity formula v_t = 2a²(ρ−σ)g/(9η) represents:
A.
The viscosity gradient
B.
The difference between sphere density and fluid density — the effective density driving the fall
C.
The compressibility of the fluid
D.
The absolute density of the sphere
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ANSWER :
B. The difference between sphere density and fluid density — the effective density driving the fall
11.
In the terminal velocity formula, the term 9η in the denominator comes from:
A.
9 × η being the product of dimensional constants
B.
Empirical measurement
C.
The nine layers of fluid around the sphere
D.
The combination of 6 (from Stokes law coefficient) and 3/2 (from simplifying 4/3 divided by 6/... = 2/9), giving 6 × 3/(2) = 9
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ANSWER :
D. The combination of 6 (from Stokes law coefficient) and 3/2 (from simplifying 4/3 divided by 6/... = 2/9), giving 6 × 3/(2) = 9
12.
Terminal velocity v_t is proportional to a² (square of radius). If the radius of a sphere is doubled, the terminal velocity becomes:
A.
2 times
B.
8 times
C.
√2 times
D.
4 times
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ANSWER :
D. 4 times