Question

A brick with dimensions of $20cm\times 10cm\times 5cm$ has a weight 500 gwt. Calculate the pressure exerted by it when it rests on different faces.

• A. Case (i) $P_1=1.25gwtc{m}^{-2}$, Case (ii) $P_2=5gwtc{m}^{-2}$, Case (iii) $P_3=5gwtc{m}^{-2}$
• B. Case (i) $P_1=2.5gwtc{m}^{-2}$, Case (ii) $P_2=5gwtc{m}^{-2}$, Case (iii) $P_3=10gwtc{m}^{-2}$
• C. Case (i) $P_1=5gwtc{m}^{-2}$, Case (ii) $P_2=25gwtc{m}^{-2}$, Case (iii) $P_3=15gwtc{m}^{-2}$
• D. Case (i) $P_1=2.5gwtc{m}^{-2}$, Case (ii) $P_2=2.5gwtc{m}^{-2}$, Case (iii) $P_3=10gwtc{m}^{-2}$

Answer 1

The correct option is B Case (i) $P_1=2.5gwtc{m}^{-2}$, Case (ii) $P_2=5gwtc{m}^{-2}$, Case (iii) $P_3=10gwtc{m}^{-2}$

Let $P_1,P_2$ and $P_3$ be the pressures exerted by the brick while resting on different faces.
The dimensions of the given brick are $20cm\times 10cm\times 5cm$
Case (i) : When the block is resting on $20cm\times 10cmface.$
Thrust acting$=$ Weight of the brick
$T=500gwt$
Area of constant $\left(A\right)=20cm\times 10cm$
Pressure exerted $\left(P_1\right)$
$=\frac{Thrust}{Area}=\frac{500}{20\times 10}$
$\therefore P_1=2.5gwtc{m}^{-2}$
Case (ii) : When the block is resting on $20cm\times 5cmface$
$Thrust=$ Weight of the brick
$=500gwt$
Area of constant $\left(A\right)=20cm\times 5cm$
Pressure exerted
$\left(P_2\right)=\frac{Thrust}{Area}=\frac{500}{20\times 5}$
$\therefore P_2=5gwtc{m}^{-2}$
Case (iii) : When the block on $10cm\times 5cmface$
$Thrust=$ Weight of the brick $=500g.wt.$
Area of contact $=10cm\times 5cm$
$Pressure=\frac{Thrust}{Area}=\frac{500}{10\times 5}$
$P_3=10gwtc{m}^{-2}$
$\therefore$ From the above three cases, it is clear that, as the area of contact decreases, the pressure exerted increases and is greater when the brick rests on its $10cm\times 5cm$ face.