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MCQEasyJEE 2026Friction (Static, Kinetic, Rolling)

JEE Physics 2026 Question with Solution

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

A vertical cylindrical drum of radius R rotates about its central vertical axis with angular velocity omega, and a block of mass M is shown pressed against the inner wall.
  • A

    μgR\sqrt{\frac{\mu g}{R}}

  • B

    gμR\sqrt{\frac{g}{\mu R}}

  • C

    2gμR\sqrt{\frac{2g}{\mu R}}

  • D

    g2μR\sqrt{\frac{g}{2\mu R}}

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: A drum of radius RR rotates with angular velocity ω\omega. A body of mass MM is pressed against the inner wall. The coefficient of friction is μ\mu.

Find: The minimum angular velocity required so that the body remains stuck to the wall.

The normal force on the body is provided by the centripetal force:

N=Mω2RN = M\omega^2 R

For the body to not slide down, the upward static friction must balance its weight:

fs=Mgf_s = Mg

The maximum available static friction is:

fs≤μNf_s \le \mu N

So, for equilibrium,

Mg≤μ(Mω2R)Mg \le \mu \left(M\omega^2 R\right)

Cancelling MM from both sides,

g≤μω2Rg \le \mu \omega^2 R

Therefore,

ω2≥gμR\omega^2 \ge \frac{g}{\mu R}

Hence the minimum angular velocity is:

ωmin⁡=gμR\omega_{\min} = \sqrt{\frac{g}{\mu R}}

Therefore, the correct option is B.

Common mistakes

  • Taking the friction force as the centripetal force is incorrect. The centripetal force is provided by the normal reaction, while friction acts vertically to prevent the mass from sliding. Use N=Mω2RN = M\omega^2 R and friction only for vertical balance.

  • Using f=μNf = \mu N without recognizing it is the maximum static friction can cause confusion. At the minimum angular velocity, the body is on the verge of slipping, so only then do we set Mg=μNMg = \mu N.

  • Forgetting that the weight acts downward and friction must act upward leads to incorrect force balance. First identify vertical equilibrium as fs=Mgf_s = Mg, then relate friction to the normal force.

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