Question

$The \: figure \: shows \\ \: a \: cube \: of \: each \: side \\ \: 15 cm \: immersed \: in \: a \\ \: tube \: containing \: water \\ \: of \: density \: 10 {}^{3} kg \: m {}^{ - 3} .$
$Calculate : \\ \ \textless \ br /\ \textgreater \ (i) \: the \: pressure \: at \: the \: top \: of \: cube, \\ \ \textless \ br /\ \textgreater \ (ii) \: the \: pressure \: at \: the \: bottom \: of \: cube, \\ \ \textless \ br /\ \textgreater \ (iii) \: the \: resultant \: thrust \: on \: cube. \\ (iv) \: the \: resultant \: thrust \: on \: cube \\ \ \textless \ br /\ \textgreater$
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Answer 1

Answer:

Pressure exerted by water on the bottom of a deep dam(Hydrostatic pressure) is 120000 Pa.

Step-by-step Explanation :

GivEn :

Density of water, ϱ = 10³kg/m³

Height = 12 m

g = 10m/s²

To find :

Pressure exerted by water on the bottom of a deep dam(Hydrostatic pressure) =

SoluTion :

We know that,

\begin{gathered}\begin{gathered}\sf \longrightarrow \: Hydrostatic \: pressure = \rho \times g \times h \\ \\\end{gathered} < /p > < p > \end{gathered}

⟶Hydrostaticpressure=ρ×g×h

</p><p>

Substituting the values,

\begin{gathered} < /p > < p > \begin{gathered}\sf \longrightarrow \: Hydrostatic \: pressure = {10}^{3} \times 10 \times 12 \\ \\\end{gathered} < /p > < p > < /p > < p > \end{gathered}

</p><p>

⟶Hydrostaticpressure=10

3

×10×12

</p><p></p><p>

\begin{gathered} < /p > < p > \begin{gathered}\sf \longrightarrow \: Hydrostatic \: pressure = {10}^{4} \times 12 \\ \\\end{gathered} < /p > < p > \end{gathered}

</p><p>

⟶Hydrostaticpressure=10

4

×12

</p><p>

\begin{gathered}\begin{gathered}\sf \longrightarrow \: Hydrostatic \: pressure = 10000 \times 12 \\ \\\end{gathered} < /p > < p > \end{gathered}

⟶Hydrostaticpressure=10000×12

</p><p>

\begin{gathered}\begin{gathered}\sf \therefore { \blue{Hydrostatic \: pressure = 120000 \: Pa}} \\ \\\end{gathered} < /p > < p > \end{gathered}

∴Hydrostaticpressure=120000Pa

</p><p>

Hence, Pressure exerted by water on the bottom of a deep dam(Hydrostatic pressure) is 120000 Pa.

Answer 2

Answer:

Given :-

Area of the triangle = 126 cm²

Base of the triangle = 56 m

To Find :-

Height of the triangle.

Solution :-

Area of the triangle :-

\green{:\implies\:\:\:}\sf{Area = \dfrac{1}{2} \times base \times height }:⟹Area=

2

1

×base×height

\green{:\implies\:\:\:}\sf{126 = \dfrac{1}{2} \times 56 \times h }:⟹126=

2

1

×56×h

\green{:\implies\:\:\:}\sf{126 = 28 \times h }:⟹126=28×h

\green{:\implies\:\:\:}\sf{h= \dfrac{126}{28} }:⟹h=

28

126

\green{:\implies \:\:\:}\underline{\boxed{\pink{\mathfrak{h = 4.5\:m}}}}:⟹

h=4.5m

∴ Height of the triangle = 4.5 m

To check ↓

Area of the triangle :-

\blue{:\implies\:\:\:}\sf{Area = \dfrac{1}{2} \times b \times h }:⟹Area=

2

1

×b×h

\blue{:\implies\:\:\:}\sf{Area = \dfrac{1}{2} \times 56 \times 4.5 }:⟹Area=

2

1

×56×4.5

\blue{:\implies\:\:\:}\sf{Area = 28 \times 4.5 }:⟹Area=28×4.5

\blue{:\implies\:\:\: }\underline{\boxed{\purple{\mathfrak{Area = 126 \:cm^2}}}}:⟹

Area=126cm

2

Hence Verified! :D