KCET 2025 Physics Paper

To determine the coefficient of viscosity of a liquid, a spherical steel ball sinks a distance of h=0.9m. The ball's radius is r=√3×10−3m. The time taken by the ball to sink as measured in three trials is shown in the table below:

Trial No.	Time to sink h (in seconds)
1	2.75
2	2.65
3	2.70

The density difference between the steel ball and the liquid is 7000‌kg∕m3, and the gravitational acceleration g=10m∕ s2. We aim to calculate the coefficient of viscosity of the liquid at room temperature.
Calculations:
Average Time:
tavg=‌

2.75+2.65+2.70

3

=2.7‌ seconds ‌
Terminal Velocity:
‌ Terminal velocity ‌=‌

h

tavg

=‌

0.9

2.7

=‌

1

3

m∕ s
Coefficient of Viscosity:
η=‌

2

9

‌

πr2g(ρ‌steel ‌−ρ‌ilquid ‌)

vt

Substituting the values,
η=‌

2

9

×‌

π×(1.732×10−3)2×10×7000

1 3

Simplifying these terms, we find:
η=0.14‌Pa. s
The coefficient of viscosity of the liquid is 0.14 Pa.s.