91Ó°ÊÓ

Fluid statics, often known as hydrostatics, is a branch of fluid mechanics that investigates the state of balance of a floating and submerged body, as well as the pressure in a fluid, or imposed by a fluid, on an immersed body.

The values we have is:

Force Applied is \[{\rm{F = 5000 N}}\].

Radius of disc is \[{\rm{2 cm = 0}}{\rm{.02 m}}\].

The cross-sectional area of disk is:

\(\begin{array}{c}A = \pi {r^2}\\ = 3.14 \times {(0.02)^2}\\ = 1.256 \times 1{0^{ - 3}}{m^2}\end{array}\)

Thickness of disk is:

\[\begin{array}{c}{\rm{L = 0}}{\rm{.800 cm}}\\{\rm{ = 0}}{\rm{.008 m}}\end{array}\]

Young’s modulus of disk is Y = \(1.5 \times 1{0^9}N/{m^2}\)

Pressure created on disk = P = ? N/m

Deformation of disk = l = ? m

\(\begin{array}{l}P = F/A\\P = 5000/(1.256 \times 1{0^{ - 3}})\\P = 3.980 \times 1{0^6}N/{m^2}\end{array}\)

Therefore, the pressure is: \[{\rm{3}}{\rm{.980 x 1}}{{\rm{0}}^{\rm{6}}}{\rm{ N/}}{{\rm{m}}^{\rm{2}}}\]

\(\begin{array}{l}Y = \frac{{F/A}}{{l/L}}\\I = \frac{{(F/A)*L}}{Y}\\I = \frac{{(3.980 \times 1{0^6})*0.008}}{{1.5 \times 1{0^9}}}\\l = \frac{{31840}}{{1.5 \times 1{0^9}}}\end{array}\)

\(\begin{array}{l}I = 2.123 \times 1{0^{ - 5}}m\\l = 0.02123mm\end{array}\)

Therefore, the deformation produced in the disk is: \[{\rm{0}}{\rm{.02123 mm}}\].