In the experiment for measurement of viscosity ' η ' of given liquid with a ball having radius R, consider following statements.
A. Graph between terminal velocity V and R will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of η will change.
Choose the correct answer from the options given below:

Solution

Physics sir · 2 steps

Write the terminal velocity formula once and test every statement against it.

1. Terminal velocity. When the ball falls at a steady speed, weight is balanced by buoyancy plus Stokes drag 6πη R v. With ρ the ball's density and σ the liquid's density, this gives the formula below.

   v = 2R²(ρ - σ)g/9η

   Statement	What the formula says	Verdict
   A	v ∝ R², so the v against R graph is a parabola	True
   B	v changes with R, so balls of different diameters have different terminal velocities	False
   C	η of a liquid falls as temperature rises, so v depends on temperature	True
   D	If η is known, measuring v lets you solve for σ, the liquid's density	True
   E	η is a property of the liquid. The ball still reaches the same terminal velocity, whatever its starting speed	False

2. So. A, C and D are correct, which is option (c).

The idea to keep. Terminal velocity goes as R²(ρ-σ)/η. Viscosity belongs to the liquid and its temperature, never to how you drop the ball.

Answer from the NTA final answer key. Solution by PrepWiser.