Question 28: Properties of Matter

Question

In the experiment for measurement of viscosity ' $\eta$ ' 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 $\eta$ will change.
Choose the correct answer from the options given below:

Accepted Answer

We know, terminal velocity of a sphere of radius R in a liquid of viscosity $\eta$,
$$v = {2 \over 9}{{{R^2}} \over \eta }(\sigma  - \rho )$$ .... (1)
where, $\sigma$ = mass of density of sphere
$\rho$ = density of liquid
we can see, $$v \propto {R^2}$$ (for constant $\eta,\sigma$ & $\rho$)
Hence, graph between v and R is parabola.
As v depends on R so the terminal velocities of different diameter balls will be different.
We know, the viscosity of a liquid usually decreases as the temperature increases and $$v \propto {1 \over \eta }$$
So terminal velocity depends on the temperature. $$T \uparrow  \Rightarrow \eta  \downarrow  \Rightarrow v \uparrow $$
As the equation $$v = {2 \over 9}{{{R^2}} \over v}(\sigma  - \rho )$$ involves density of liquid $\rho$. So the experiment can be utilized to asses it.
From (1), $$\eta  = {2 \over 9}{{{R^2}} \over v}(\sigma  - \rho )$$
Here, $\eta$ does not depend on initial speed of the sphere. Hence, option 3 is correct.

Answer

C, D and E Only

Answer

A, B and E Only

Answer

A, C and D Only

Answer

B, D and E Only

Properties of Matter

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