Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202227 JuneMorning Shift
Exam
JEE Main
Year
2022
Date
27 June
Shift
Morning Shift
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Main 2022 · 27 June · Morning Shift · Physics · Mechanical Properties of Fluids

The velocity of a small ball of mass m and density d _ 1 , when...

The velocity of a small ball of mass mm and density d1{d}_{1}, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is d2{d}_{2}, then the viscous force acting on the ball, will be

Options

  1. Amg(1−d1d2)mg\left(1 - \dfrac{{d}_{1}}{{d}_{2}}\right)
  2. Bmg(1−d2d1)mg\left(1 - \dfrac{{d}_{2}}{{d}_{1}}\right)
  3. Cmg(d1d2−1)mg\left(\dfrac{{d}_{1}}{{d}_{2}} - 1\right)
  4. Dmg(d2d1−1)mg\left(\dfrac{{d}_{2}}{{d}_{1}} - 1\right)

Correct answer

B. mg(1−d2d1)mg\left(1 - \dfrac{{d}_{2}}{{d}_{1}}\right)

Step-by-step solution

At the time of terminal velocity ball is in equilibrium i.e. Fg=Fb+Fv{F}_{g} = {F}_{b} + {F}_{v}

⇒Fv=Fg−Fb⇒ {F}_{v} = {F}_{g} - {F}_{b}

⇒Fv=mg−d2md1g⇒ {F}_{v} = mg - {d}_{2}\dfrac{m}{{d}_{1}}g

⇒mg(1−d2d1)⇒ mg\left(1 - \dfrac{{d}_{2}}{{d}_{1}}\right)

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… JEE Advanced 2026A liquid of density 600 kg/m ^3 flowing steadily in a tube of varying cross-section. The… JEE Main 2026A spherical liquid drop of radius R acquires the terminal velocity v_1 when falls through… JEE Main 2026A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is… JEE Main 2026Eight mercury drops, each of radius r , coalesce to form a bigger drop. The surface… JEE Main 2026A water spray gun is attached to a hose of cross sectional area 30 cm ^2 . The gun… JEE Main 2026The surface tension of a soap solution is 3.5 × 10^ -2 N/m. The work required to increase… JEE Main 2026The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the… JEE Main 2026 Full Mechanical Properties of Fluids list All JEE Main PYQs