Question

A cube of edge length 5 cm is placed inside a liquid. The pressure at the centre of a face is 12 Pa. Findthe force exerted by the liquid on this face,
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Answer 1

Answer:

Given :-

• A cube of edge length is 5 cm is a placed inside a liquid.
• The pressure at the centre of a face is 12Pa.

To Find :-

• What is the force exerted by the liquid on this face.

Formula Used :-

$\clubsuit$ Force Formula :

$\mapsto \sf\boxed{\bold{\pink{Force =\: Pressure \times Area}}}$

Solution :-

First, we have to convert side of face cm into m :

$\implies \sf Side =\: 5\: cm$

$\implies \sf Side =\: \dfrac{5}{100}\: m$

$\implies\sf\bold{\purple{Side =\: 0.05\: m}}$

Now, we have to find the area of face :

As we know that :

$\bigstar\: \: \: \sf\bold{\pink{Area_{(Face)} =\: (Side)^2}}\: \: \bigstar$

Given :

• Side = 0.05 m

According to the question by using the formula we get,

$\implies \sf Area_{(Face)} =\: (0.05)^2$

$\implies \sf Area_{(Face)} =\: 0.05 \times 0.05$

$\implies \sf\bold{\green{Area_{(Face)} =\: 0.0025\: m^2}}$

Now, we have to find the force exerted by the liquid on this face :

Given :

• Pressure = 12Pa
• Area = 0.0025 m²

According to the question by using the formula we get,

$\longrightarrow \sf Force =\: 12 \times 0.0025$

$\longrightarrow \sf\bold{\red{Force =\: 0.03\: N}}$

${\small{\bold{\underline{\therefore\: The\: force\: exerted\: by\: the\: liquid\: is\: 0.03\: N\: .}}}}$

Answer 2

$\pink{ \boxed{\boxed{\begin{array}{cc} \maltese  \bf \: given \: \\ \\ \rm \to \: Pressure \: = \: P \: =12 \: Pa \\ \\ \rm \to \: edge \: length \: of \: the \: cube \: a = 5 \: cm \\ \\ \bf \odot \: we \: have \: to \: find \: : \\ \\ \small{ \boxed{\rm \to \: Force \: exerted \: by \: the \: liquid \: on \: the \: face \: = F}} \\ \\ \end{array}}}}$

At first we have to find the area (A) of that face.

$\rm \: Area \: of \: \: one \: face \:of \: the \: cube ,\\ \rm \: A = {a}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm = 5 \times 5 \:{cm}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm = 25 \times {10}^{ - 4} \: {m}^{2}$

Now,

$\pink{ \boxed{\boxed{\begin{array}{cc} \maltese  \bf \: we \: know \: that \\\\\rm\:Pressure \: (P ) = \frac{Force(F)}{Area(A)} \\ \\ \rm \implies \:F=PA\\\\ \rm \implies \:F=12 \times 25 \times {10}^{ - 4} \\ \\\rm \implies \: F=0.03 \: N \end{array}}}}$

So,

$\small{{ \boxed{\boxed{\begin{array}{cc} \small{ \maltese  \rm \: Force \: exerted \: by \: the \: liquid \: on \: that \: face \: \: is  \: F=0.03 \: N}\end{array}}}}}$