Question

terminal velocity is more if surface area of the body is more.Give reason and support your answer​

Answer 1

Answer:

Yes, Terminal velocity of a body is more when surface area of a body is more. <br> According to Stokes formula, terminal velocity of a smooth spherical body is, <br>

Vt=2/9r²g[p-p0/n]

<br> the surface area of a spherical body

. So when surface increases ,

' value increases. Hence from Stoke's formula, Terminal velocity increases.

Answer 2

Yes, terminal velocity is more if the surface area of the body is more.

What is terminal velocity?

• When an object is falling through a viscous liquid, it experiences the following forces:

1. Buoyant Force = ρVg upwards
2. Viscous Force = 6πηrv upwards
3. Weight = mg = (σV)g downwards

where ρ is the density of the liquid

          V is the volume of the liquid displaced by the object

          η is the coefficient of viscosity

          r is the radius of the object

          v is the velocity of the object

  and σ is the density of the object

• As the object continues falling farther into the liquid, eventually all 3 forces neutralize each other and the net force becomes 0.
• Thus the body has 0 acceleration and attains a constant velocity.
• This constant velocity is called the terminal velocity. ($v_{t}$).

What is the formula for terminal velocity?

• When we balance all the forces acting on the object, we get:

                         ρVg + 6πηrv = σVg

Solving this equation, we get the following relation:

                           $v_{t}$ = $\frac{2}{9}$ × $\frac{r^{2}g }{n}$ × (ρ - σ)                    (1)

So from this formula, we can draw the following conclusions about terminal velocity:

1. It is directly proportional to the square of the radius of the object.
2. It is directly proportional to the difference in the densities of the object and liquid.

What happens when the surface area of the body increases?

• Assuming the object to be a perfect sphere, its surface area will be given by:

                              A = 4πr²

• Hence, a larger surface area implies a larger radius.
• From equation (1), we know that terminal velocity increases as radius increases.

So, the terminal velocity will increase as the surface area of the body increases.

Hence, proved.