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The neck and bottom of a bottle are 3 cm and 15 cm in radius respectively. If the cork is pressed with a force 12 N in the neck of the bottle, then force exerted on the bottom of the bottle is
  • a)
    30 N
  • b)
    150 N
  • c)
    300 N
  • d)
    600 N
Correct answer is option 'C'. Can you explain this answer?
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The neck and bottom of a bottle are 3 cm and 15 cm in radius respectiv...
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The neck and bottom of a bottle are 3 cm and 15 cm in radius respectiv...
Given:
Neck radius, r1= 3 cm
Bottom radius, r2= 15 cm
Force applied on cork, F1= 12 N

To find: Force exerted on the bottom of the bottle, F2

Formula used:

Pressure = Force / Area

Area of the neck, A1= πr1²
Area of the bottom, A2= πr2²

As the bottle is filled with liquid, the pressure is transmitted equally in all directions.

Therefore,

Pressure at the neck = Pressure at the bottom

Or,

F1/A1 = F2/A2

Substituting the values, we get

12/π(3)² = F2/π(15)²

F2 = 12/π(3)² * π(15)²

F2 = 300 N

Hence, the force exerted on the bottom of the bottle is 300 N.

Therefore, the correct option is (c) 300 N.
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