Two vertical parallel rectangular glass plates are partially submerged in water. The separation between the plates is $d = 0.2 m m$ and the width of each plate is $l = 10 c m .$ Assume that the water between the plates does not reach the upper edges of the plates and the contact angle is $θ = 0 ° .$ The surface tension of water is $T = 7 \times 10^{- 2} N / m$ and the density of water is $ρ = 10^{3} k g / m^{3} .$ Then choose the CORRECT option(s). $(g = 10 m / s^{2})$

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The water rises upto height $h = 7 c m$ between the plates

The water rises upto height $h = 14 c m$ between the plates

The force of mutual attraction between the plates is $9.8 N$

The force of mutual attraction between the plates is $2.45 N$

answer is A, C.

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Detailed Solution

$2 T l = ρ d l h g h = \frac{2 T}{ρ g d} = \frac{2 \times 7 \times 10^{- 2}}{10^{3} \times 10 \times 2 \times 10^{- 4}} = 7 \times 10^{- 2} m = 7 c m$

Force of mutual attraction between the plats is

$F = \int_{0}^{h} ρ g y l d y = \frac{ρ g l h^{2}}{2} = \frac{10^{3} \times 10 \times 0.10 \times {(7 \times 10^{- 2})}^{2}}{2} = \frac{4.9}{2} = 2.45 N$