Question

Which will exert more pressure, $100kg$ mass on $10m^2$ or $50kg$ on $4m^2$ ? Give reason.

Answer 1

Step 1: Formula used

The force acting on the unit area of the surface is called pressure.

Pressure $\mathbf{=}\frac{\mathbf{F}\mathbf{o}\mathbf{r}\mathbf{c}\mathbf{e}\mathbf{\left(}\mathbf{F}\mathbf{\right)}}{\mathbf{A}\mathbf{r}\mathbf{e}\mathbf{a}\mathbf{\left(}\mathbf{A}\mathbf{\right)}}$

From Newton's second law

Force (F) $\mathbf{=}\mathit{m}\mathit{a}\mathit{s}\mathit{s}\mathbf{}\mathbf{\left(}\mathit{m}\mathbf{\right)}\mathbf{\times }\mathit{a}\mathit{c}\mathit{c}\mathit{e}\mathit{l}\mathit{e}\mathit{r}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathbf{\left(}\mathit{a}\mathbf{\right)}$

Acceleration due to gravity $=10m/s$

Step 2: Comparing pressures

${\mathit{P}}_{\mathbf{1}}\mathbf{=}\frac{{\mathbf{F}}_{\mathbf{1}}}{{\mathbf{A}}_{\mathbf{1}}}\mathbf{=}\frac{{\mathbf{m}}_{\mathbf{1}}\mathbf{g}}{{\mathbf{A}}_{\mathbf{1}}}$

${\mathit{P}}_{\mathbf{1}}\mathbf{=}\frac{\mathbf{100}\mathbf{\times }\mathbf{10}}{\mathbf{10}}$

${\mathit{P}}_{\mathbf{1}}\mathbf{=}\mathbf{100}\mathbf{}\mathit{P}\mathit{a}$

${\mathit{P}}_{\mathbf{2}}\mathbf{=}\frac{{\mathbf{F}}_{\mathbf{2}}}{{\mathbf{A}}_{\mathbf{2}}}\mathbf{=}\frac{{\mathbf{m}}_{\mathbf{2}}\mathbf{g}}{{\mathbf{A}}_{\mathbf{2}}}$

$\mathbf{=}\frac{\mathbf{50}\mathbf{\times }\mathbf{10}}{\mathbf{4}}$

${\mathit{P}}_{\mathbf{2}}\mathbf{=}\mathbf{125}\mathit{P}\mathit{a}$

As ${\mathit{P}}_{\mathbf{2}}\mathbf{>}{\mathit{P}}_{\mathbf{1}}$

Therefore, $50kg$ on $4m^2$will exert more pressure.