Physics · Mechanical Properties of Matter

JEE Main 2024 — 31 January, Shift 2 — Question 45

A small spherical ball of radius $r$ , falling through a viscous medium of negligible density has terminal velocity ' $v$ '. Another ball of the same mass but of radius 2 r , falling through the same viscous medium will have terminal velocity:

Option A:
$\frac{v}{2}$
Correct
Option B:
$\frac{v}{4}$
Option C:
4 v
Option D:
2 v

Answer: A

Step-by-step solution

Since density is negligible hence Buoyancy force will be negligible At terminal velocity.

$\mathrm{Mg}=6 \pi \eta \mathrm{rv}$ $\mathrm{V} \propto \frac{1}{\mathrm{r}} \quad \text { (as mass is constant) }$

Now, $\frac{\mathrm{v}}{\mathrm{v}^{\prime}}=\frac{\mathrm{r}^{\prime}}{\mathrm{r}}$

$r^{\prime}=2 r$ So, $\mathrm{v}^{\prime}=\frac{\mathrm{v}}{2}$

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: 31 January, Shift 2
Subject: Physics
Chapter: Mechanical Properties of Matter
Topic: Viscosity

Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is 4.0 ×…

Answer: A

Step-by-step solution

Practise Mechanical Properties of Matter

More Mechanical Properties of Matter questions from this paper