A large drum having radius R is spinning around its axis with angular velocity ω , as shown in figure. The minimum value of ω so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M is μ , is :

Physics · Horizontal Circular Motion

JEE Main 2026 — 21 January, Evening Shift — Question 41

A large drum having radius R is spinning around its axis with angular velocity $\omega$ , as shown in figure. The minimum value of $\omega$ so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M is $\mu$ , is :

Option A:
$\sqrt{\frac{\mu \mathrm{g}}{\mathrm{R}}}$
Option B:
$\sqrt{\frac{2 \mathrm{~g}}{\mu \mathrm{R}}}$
Option C:
$\sqrt{\frac{g}{2 \mu R}}$
Option D:
$\sqrt{\frac{g}{\mu R}}$
Correct

Answer: D

Step-by-step solution

\begin{aligned} & \mathrm{N}=\mathrm{m} \omega^{2} \mathrm{r}, \mathrm{mg}=\mu \mathrm{N} & \mu \times \mathrm{m} \omega^{2} \mathrm{r}=\mathrm{mg} & \omega=\sqrt{\frac{\mathrm{g}}{\mu \mathrm{r}}} \end{aligned}

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 21 January, Evening Shift
Subject: Physics
Chapter: Horizontal Circular Motion
Topic: Dynamics of circular motion