Question

As shown in the figure, forces of ${10}^{5}N$ each are applied in opposite directions, on the upper and lower faces of a cube of side $10cm$, shifting the upper face parallel to itself by $0.5cm$. If the side of another cube of the same material is $20cm$, then under similar conditions as above, the displacement will be:

• A. $1.00cm$
• B. $0.25cm$
• C. $0.37cm$
• D. $0.75cm$

Answer 1

The correct option is B $0.25cm$

For same material the ration of stress to strain is same

For first cube

$Stres{s}_1=\frac{{10}^5}{\left({0.1}^2\right)}$

$strai{n}_1=\frac{0.5\times {10}^{-2}}{0.1}$

For second block,

$stres{s}_2=\frac{{10}^5}{(0.2{)}^2}$

$strai{n}_2=\frac{x}{0.2}$

where x is the displacement for second block.

For same material,

$\frac{stres{s}_1}{strai{n}_1}=\frac{stres{s}_2}{strai{n}_2}$

From this $x=0.25cm$