Question

A spherical ball of radius r is allowed to fall from rest in long viscous medium find exponent of r on emwhich heat depende at the point when sphere attains terminal velocity

Answer 1

1. Question⇒  A spherical ball of radius r is allowed to fall from rest in long viscous medium find exponent of r on emwhich heat depende at the point when sphere attains terminal velocity

Explanation:

• The forces acting on the sphere are :
• Weight = 4/3πr³рg downwards
• Buoyant force = 4/3πr³бg upwards
• Viscous force = 6πηrν upwards
• The sphere attains the terminal velocity v₍t₎ when the resultant force acting on it is zero. i-e,
• 4/3πr³рg = 4/3πr³бg + 6πηrv₍t₎
• Solving above equation gives us the terminal velocity,
• v₍t₎ = 2r²(р-б)g / 9η
• The rate of heat generation is equal to the rate of work done by the viscous force which in turn is equal to its power. Thus,
• dQ/dt = (6πηrv₍t₎) v₍t₎ = 8π(р-б)²g²r⁵ / 27η