Name: Capillary Rise
Uploaded: 2019-07-19
Duration: 10 min 29 s
Description: Have you ever seen what happens to a celery stalk dipped in red-coloured water? We notice that after a day or two, the leaves turn reddish! Let's learn the r...

Question

A glass plate of length $50 cm$ , breadth $40 cm$ and thickness $5 cm$ weighs $3 kg$ in air. If it is held vertically with long side horizontal and the plate half immersed in a liquid, what will be its apparent weight? Surface tension of the liquid $= 50 \times 10^{- 2} N m^{- 1}$

Accepted Answer

Given, length $l = 50 cm = 50 \times 10^{- 2} m;$ breadth, $b = 40 cm = 40 \times 10^{- 2} m;$ thickness $t = 5 cm = 5 \times 10^{- 2} m;$ mass of glass plate, $m = 3 kg$ and tension, $T = 50 \times 10^{- 3} N m^{- 2}$

The glass plate is under the action of the following forces
$(i)$ Weight $W$ acting vertically downwards,
$(i i)$ Force due to surface tension $F_{T}$ acting vertically downwards and
$(i i i)$ Upward thrust $F_{U}$ experienced due to the half immersed part of the plate.

Thus, apparent weight $W^{'}$ of the glass plate is given by

$W^{'} = W + F_{T} - F_{U}$ ... $(1)$

Now, weight of the glass plate, $W = m g = 3 \times 10 = 30 N$

Length and thickness of both side of the glass plate are in contact with surface of liquid. Therefore, force due to surface tension is given by

$F_{T} = T \times 2 (l + t) = (50 \times 10^{- 3}) \times 2 (50 \times 10^{- 2} + 5 \times 10^{- 2}) = 0.055 N$

Let, $V$ be volume of liquid having density $ρ_{l i q u i d}$ displaced by immersed portion of the glass plate, then upward thrust acting on the glass plate is given by

$F_{U} = ρ_{l i q u i d} V g = ρ_{l i q u i d} \times (l \times t \times \frac{b}{2}) \times g$

$\Rightarrow F_{U} = ρ_{l i q u i d} \times (50 \times 10^{- 2} \times 5 \times 10^{- 2} \times \frac{40 \times 10^{- 2}}{2}) \times 10 = 0.05 ρ_{l i q u i d}$

Substituting above values in equation $(1)$ , we get

Apparent weight, $W^{'} = 30 + 0.055 - 0.05 ρ_{l i q u i d} = 30.055 - 0.05 ρ_{l i q u i d}$

A glass plate of length $50 cm$ , breadth $40 cm$ and thickness $5 cm$ weighs $3 kg$ in air. If it is held vertically with long side horizontal and the plate half immersed in a liquid, what will be its apparent weight? Surface tension of the liquid $= 50 \times 10^{- 2} N m^{- 1}$

Important Questions on Surface Tension and Viscosity

Learn and Prepare for any exam you want !

A glass plate of length 50 cm, breadth 40 cm and thickness 5 cm weighs 3 kg in air. If it is held vertically with long side horizontal and the plate half immersed in a liquid, what will be its apparent weight? Surface tension of the liquid =50×10-2 N m-1

Important Questions on Surface Tension and Viscosity

Learn and Prepare for any exam you want !

A glass plate of length $50 cm$ , breadth $40 cm$ and thickness $5 cm$ weighs $3 kg$ in air. If it is held vertically with long side horizontal and the plate half immersed in a liquid, what will be its apparent weight? Surface tension of the liquid $= 50 \times 10^{- 2} N m^{- 1}$