A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is , then the excess force required to take it away from the surface is [2024]

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Solution

Q.
A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is $0.07$ ${Nm}^{- 1}$ , then the excess force required to take it away from the surface is [2024]

1 19.8 mN

2 198 N

3 1.98 mN

4 99 N

Ans.
(1)

Surface tension of water, $T = 0.07$ $N$ $m^{- 1}$

Radius of disc, $r = 4.5$ cm

Required excess pressure, $P = \frac{2 T}{r}$

$∴$ Required force to take it away from the surface is $F = (P) \times Area$

or $F = \frac{2 T}{r} \times π r^{2} = 2 \times T \times (π r)$

$= 2 \times 0.07 \times 3.14 \times 4.5 \times 10^{- 2} = 1.978 \times 10^{- 2} = 19.8 mN$

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