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 as $μ,$ is: [2026]

Question

Smart Achievers · Accepted Answer

(3)

$N = m ω^{2} r, m g = μ N$

$μ \times m ω^{2} r = m g$

$ω = \sqrt{\frac{g}{μ r}}$

Solution

Q.
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 as $μ,$ is: [2026]

1 $\sqrt{\frac{μ g}{R}}$

2 $\sqrt{\frac{g}{2 μ R}}$

3 $\sqrt{\frac{g}{μ R}}$

4 $\sqrt{\frac{2 g}{μ R}}$

Ans.
(3)

$N = m ω^{2} r, m g = μ N$

$μ \times m ω^{2} r = m g$

$ω = \sqrt{\frac{g}{μ r}}$

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Solution

Q. 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 as μ, is: [2026]

1 μgR

2 g2μR

3 gμR

4 2gμR

Ans. (3) N=mω2r, mg=μN μ×mω2r=mg ω=gμr