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  • A spherical metal ball has a diameter (d) of 0.04 meters, and its coefficient of viscosity in a liquid is 0.8 Ns/m². The ball experiences a terminal acceleration (v) of 0.1 m/s² while mov

A spherical metal ball has a diameter (d) of 0.04 meters, and its coefficient of viscosity in a liquid is 0.8 Ns/m². The ball experiences a terminal acceleration (v) of 0.1 m/s² while moving through the liquid. Use this information to measure the coefficient of viscosity in standard units.

Option: 1

1.60Ns/m2


Option: 2

 8.70Ns/m2


Option: 3

0.8Ns/m2


Option: 4

20Ns/m2


Answers (1)

best_answer

Given information:

Diameter of the ball (d) = 0.04 meters

Coefficient of viscosity (η) = 0.8 Ns/m2

Terminal acceleration (v) = 0.1 m/s2

To measure the coefficient of viscosity, we can use Stokes’ law equation:

F_{\text {drag }}=6 \pi \eta r v     (1)

Where:

Fdrag is the drag force on the ball

η is the coefficient of viscosity

r is the radius of the ball

v is the terminal acceleration

The radius is half the diameter:

r=\frac{d}{2}=\frac{0.04}{2}=0.02 \mathrm{~m}

Using equation (1), we rearrange to solve for η:

\eta=\frac{F_{\mathrm{drag}}}{6 \pi r v}

Plugging in values:

\eta=\frac{F_{\text {drag }}}{6 \pi \times 0.02 \mathrm{~m} \times 0.1 \mathrm{~m} / \mathrm{s}^2}=0.8 \mathrm{Ns} / \mathrm{m}^2

The coefficient of viscosity is found to be 0.8 Ns/m2 based on the terminal acceleration of the spherical metal ball moving through the liquid. Therefore, the correct option is C.

Posted by

Divya Prakash Singh

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