JEE Main 2016 · 10 Apr · Shift 1 · Physics Q7

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PhysicsSingle correct+4 / -1Question 7 of 90

A bottle has an opening of radius a and length b. A cork of length b and radius (a + Δa) where (Δa << a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is μ then the force needed to push the cork into the bottle is :

A bottle whose neck of radius a and length b is filled by a cork of length b.

(\pi\mu Bb)\Delta a

(2\pi\mu Bb)\Delta a

(\pi\mu Bb)a

(4\pi\mu Bb)\Delta a

Answer and worked solution

Official answer: D

The volumetric strain is $\frac{\Delta V}V=\frac{2\Delta a}a$ , so the pressure on the neck is $P=B\frac{2\Delta a}a$ . The normal force on the curved surface is $P\cdot2\pi ab$ , and the friction to overcome is
$\mu\cdot\frac{2B\Delta a}a\cdot2\pi ab=4\pi\mu Bb\,\Delta a.$

Topics:Hooke's law and elastic moduli Friction

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JEE Main 2016 · 10 Apr · Shift 1, Physics question 7