NTA Abhyas JEE Main2020PhysicsMechanical Properties of SolidsPractice
A bottle has an opening of radius a and length b . A cork of length b and radius a + ∆ a where ∆ a ≪ a , is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is B and the coefficient of friction between the bottle and cork is μ , then the force needed to push the cork into the bottle is
Options
- AπμBb a
- B2 πμBb ∆ a
- CπμBb ∆ a
- D4 πμBb ∆ a
Correct answer
D. 4 πμBb ∆ a
Step-by-step solution
Pressure = N A = N 2 πa b ⇒      stress = B × strain   N 2 πa b = B 2 πa ∆ a × b   πa 2 b ⇒ N = B f = μN = μ 4 πbBΔa