A small ball of mass m and density ρ is dropped in a viscous liquid of density ρ 0 . After sometime, the ball falls with constant velocity. The viscous force on the ball is :

Physics · Mechanical Properties of Matter

JEE Main 2024 — 6 April, Shift 1 — Question 49

A small ball of mass $m$ and density $\rho$ is dropped in a viscous liquid of density $\rho_{0}$ . After sometime, the ball falls with constant velocity. The viscous force on the ball is :

Option A:
$\operatorname{mg}\left(\frac{\rho_{0}}{\rho}-1\right)$
Option B:
$\operatorname{mg}\left(1+\frac{\rho}{\rho_{0}}\right)$
Option C:
$\operatorname{mg}\left(1-\rho \rho_{0}\right)$
Option D:
$\operatorname{mg}\left(1-\frac{\rho_{0}}{\rho}\right)$
Correct

Answer: D

Step-by-step solution

$\mathrm{mg}-\mathrm{F}_{\mathrm{B}}-\mathrm{F}_{\mathrm{v}}=\mathrm{ma}$

$\mathrm{a}=0$ for constant velocity

$m g-F_{B}=F_{v}$ $\mathrm{F}_{\mathrm{v}}=\mathrm{mg}-\mathrm{v} \rho_{0} \mathrm{~g}=\mathrm{mg}-\frac{\mathrm{m}}{\rho} \rho_{0} \mathrm{~g}=\mathrm{mg}\left(1-\frac{\rho_{0}}{\rho}\right)$

Answer key and solution verified before publishing.

Practise Mechanical Properties of Matter

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2024
Paper: 6 April, Shift 1
Subject: Physics
Chapter: Mechanical Properties of Matter
Topic: Viscosity

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop…

Answer: D

Step-by-step solution

Practise Mechanical Properties of Matter

More Mechanical Properties of Matter questions from this paper