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Question

Two vertical parallel glass plates are partially submerged in water. The distance between the plates is d=0.10mm, and their width is l=12cm. Assuming that the water between the plates does not reach the upper edges of the plates and that the wetting is complete, find the force of their mutual attraction.

A
17N
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B
13N
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C
10
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D
19N
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Solution

The correct option is B 13N
Given: d=0.10mm ; l=12cm
Solution: The energy of the liquid between the
plates is


E=ldhρgh22αlh
=12ρgldh22αlh
=12ρgld(h2αρgd)22α2lρgd


This energy is minimum when,

h=2αρgd and

the minimum potential energy is then Emin

=2α2lρgd

The force of attraction between the
plates can be obtained from this as

F=Emind=2α2lρgd2
$
(minus sign means the force is attractive.)
Thus

F=αlhd=13 N
So,the correct option:B


2011570_995671_ans_dcd09606565846db828c2c0c346084d0.jpeg

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