Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Highly selective Backlog Qs for JEE MainPhysicsMechanical Properties of Fluids

A small sphere of radius r falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains terminal velocity, is proportional to

Options

  1. Ar 5
  2. Br 2
  3. Cr 3
  4. Dr 4

Correct answer

A. r 5

Step-by-step solution

Rate of heat produced = power of viscous force terminal velocity V T = 2 r 2 ( ρ − σ ) g 9 η ⇒ V T ∝ r 2 d Q d t = 6 πη r V T × V T ⇒ d Q d t ∝ r 5

Practice Mechanical Properties of Fluids on Quantrex Academy →

More from Mechanical Properties of Fluids

Passage: A container of height 2 m, length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates ( M₁ and M₂ ) which extend far beyond 2026A liquid of density 600 kg/m ^3 flowing steadily in a tube of varying cross-section. The cross-section at a point A is 1.0 cm ^2 and that at B is 20 mm ^2 . Both the points A and B 2026A spherical liquid drop of radius R acquires the terminal velocity v₁ when falls through a gas of viscosity . Now the drop is broken into 64 identical droplets and each droplet acq 2026A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is 528 dm ^3 (dm : decimeter). The vessel is placed on a solid block of exactly same height as 2026Eight mercury drops, each of radius r , coalesce to form a bigger drop. The surface energy released in this process is _______. ( S is the surface tension of mercury). 2026A water spray gun is attached to a hose of cross sectional area 30 cm ^2 . The gun comprises of 10 perforations each of cross sectional area 15 mm ^2 . If the water flows in the ho 2026The surface tension of a soap solution is 3.5 10⁻² N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is 10⁻⁶ J. The value of is _____. ( = 22/7 ) 2026The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is 10⁻⁴ J. The value of is _______. (Take = 3.14 ) 2026 Full Mechanical Properties of Fluids list All Highly selective Backlog Qs for JEE Main PYQs