Question:

A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :

Updated On: Jan 18, 2023
  • $\eta_{_0} $ only
  • $\eta_{_W} $ only
  • both on $\eta_{_0}$ and $\eta_{_W}$
  • neither $\eta _{_0}$ nor $\eta _{W}$
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The Correct Option is B

Solution and Explanation

Answer (b) $\eta_{_W} $ only
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Concepts Used:

Pressure

Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

Everyday examples of pressure are:

  • The working of the vacuum cleaner is an example of pressure. The fan inside the vacuum creates a low-pressure region which makes it easy to suck the dust particles inside the vacuum.
  • Using a knife for cutting is another example of pressure. The area exposed from the knife is small but the pressure is high enough to cut the vegetables and fruits.

Formula:

When a force of ‘F’ Newton is applied perpendicularly to a surface area ‘A’, then the pressure exerted on the surface by the force is equal to the ratio of F to A. The formula for pressure (P) is:

P = F / A

Units of Pressure:

The SI unit of pressure is the pascal (Pa)

A pascal can be defined as a force of one newton applied over a surface area of a one-meter square.