To Determine The Coefficient Viscosity Of A Given Viscous Liquid By Measuring The Terminal Velocity Of Given Spherical Body - Practice Questions & MCQ

Aim
To determine the coefficient of viscosity of a given viscous liquid by measuring the terminal velocity of a given spherical body.

Apparatus
A half metre high,  5 cm broad glass cylindrical jar with millimetre graduations along its height, transparent viscous liquid, one steel ball, screw gauge, stop clock/watch, thermometer, clamp with stand.

Theory

$
\eta=\frac{2}{9}(\rho-\sigma) g \frac{r^2}{v}
$

$\eta=$ coefficient of viscosity
$\rho=$ density of ball
$\sigma=$ density of liquid

r= radius of ball

v= terminal velocity of ball

Knowing r,  and , and measuring v,  can be calculated.

Procedure

1.    Take some viscous liquid which must be homogeneous and transparent.

2.    Clean the glass cylinder and fill it with this liquid.

3.    Find the least count of the vertical scale (graduation) of the glass cylinder.

4.    Find the least count and zero error of the stop watch.

5.    Find the least count and zero error of the screw gauge.

6.    Mark the given balls as 1, 2, 3, 4, 5. Giving number 1 to the ball of smallest diameter and number 5 to the ball of maximum diamter.

7.    Find the diameters of the balls as explained in Experiment 2. (Section A)

8.    Make two convenient marks o the cylinder about 40 cm apart, one at a distance of 40 cm from top and other at a distance of 20 cm from bottom.

9.    Drop the ball 1 gently in the liquid. For about 1/3^rd of the height of the liquid column, ball falls down with the accelerated velocity. After that this ball falls down with the uniform velocity called terminal velocity. 

10.    When ball covers about 40 cm from the top, start the stop watch.

11.    Stop the stop watch when ball reaches the lower mark which is at 20 cm from the bottom.

12.    Note the distance covered by the ball and time taken to cover this distance.

13.    Repeat the experiment one more time with the steel ball of same diameter.

14.    Repeat the steps 9 to 13 with other four balls also.

Calculation - 

Mean diameter

$
D=\frac{D_1+D_2}{2} \mathrm{~mm}
$

Mean radius

$
r=\frac{D}{2} \mathrm{~mm}=
$

$\qquad$ .cm

Mean time

$
t=\frac{t_1+t_2+t_3}{3}=
$

$\qquad$
Mean terminal velocity, $\quad v=\frac{S}{t}=\ldots \mathrm{cms}^{-1}$
From formula,
$\eta=\frac{2 r^2(\rho-\sigma) g}{9 v}=$ $\qquad$ C.G.S. units

Precautions -

1. Liquid should be transparent to watch motion of the ball.
2. Ball should be perfectly spherical.
3. Velocity should be noted only when it becomes constant.