Question

A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of
coefficient of viscosity n. After some time the velocity of the ball attains a constant value known as
terminal velocity Op. The terminal velocity depends on (i) the mass of the ball m, (i) n. (i) r and (iv)
acceleration due to gravity g. Which of the following relations is dimensionally correct?
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Answer 1

                                Terminal Velocity:

Definition of terminal velocity: Terminal velocity can be defined as the maximum attainable velocity that an object falling through a fluid can achieve.

Terminal velocity is attained when the resistive force of the fluid, also known as the drag force and the buoyancy of the fluid equals the force of gravity acting on the object downwards.

Terminal velocity depends on the following factors:

1) The mass of the object, m

2) The projected area of the falling object, A

3) The acceleration due to gravity, g

4) The drag coefficient/ coefficient of viscosity, n

5) The density of the fluid, d

The formula of the calculating the terminal velocity:

  Terminal velocity = $\sqrt{\frac{2mg}{dAn}}$

Answer 2

Explanation:

Terminal Velocity:

Definition of terminal velocity: Terminal velocity can be defined as the maximum attainable velocity that an object falling through a fluid can achieve.

Terminal velocity is attained when the resistive force of the fluid, also known as the drag force and the buoyancy of the fluid equals the force of gravity acting on the object downwards.

Terminal velocity depends on the following factors:

1) The mass of the object, m

2) The projected area of the falling object, A

3) The acceleration due to gravity, g

4) The drag coefficient/ coefficient of viscosity, n

5) The density of the fluid, d