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 :

(A) $\sqrt{\frac{\mu \mathrm{g}}{\mathrm{R}}}$

(B) $\sqrt{\frac{2 \mathrm{~g}}{\mu \mathrm{R}}}$

(C) $\sqrt{\frac{g}{2 \mu R}}$

JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Laws of Motion

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

μ

, is :

(A) $\frac{μ g}{R}$
(B) $\frac{2 g}{μ R}$
(C) $\frac{g}{2 μ R}$
(D) $\frac{g}{μ R}$ ✓ Correct

Answer: (D)

Solution

For the body to remain stuck, the frictional force must balance the weight. The normal force is

N = m ω^{2} R

, and the friction is

f = μ N = μ m ω^{2} R

. For equilibrium:

m g = μ m ω^{2} R

. Solving for

ω

ω = \frac{g}{μ R}

JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Single correct option

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