Question

A small metal sphere of mass M and density d₁, when dropped in a jar filled with liquid moves with terminal velocity after sometime. The viscous force acting on the sphere is (d₂ = density of liquid and g = gravitational acceleration)

Options

• `"Mg"("d"_1/"d"_2)`

• `"Mg"(1-"d"_2/"d"_1)`

• `"Mg"("d"_2/"d"_1)`

• `"Mg"(1-"d"_1/"d"_2)`

Answer 1

`"Mg"(1-"d"_2/"d"_1)`

Explanation:

The motion of metal sphere is shown as

 

where F_B = Buoyant force and F_v = viscous force.

At terminal velocity, the net force on the sphere is zero.

W = F_B +F_V

⇒  Mg =d₂Vg + F_v

`="d"_2"M"/"d"_1"g"+"F"_"V"`

`therefore "F"_"V"="Mg"(1-"d"_2/"d"_1)`