Question

Question:
A uniform cubical block is subjected to volumetric compression, which decreases its each side by 2%. The Bulk strain produced in it is
1) 0.03
2) 0.02
3) 0.06
4) 0.12

Answer 1

$\underline{\underline{\Huge\mathfrak{Answer ;}}}$

Dear ,

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Given that ;-
• Lenght's percentage change = 2%

So now ,
Assuming the side of Cube as M.

Then ,
Volume = V = M^3

Hence ,

∆ V/ V = 3× ∆ M / M

So , Volume's percentage change = Lenght's percentage change × 3.

Now ,
Volume's percentage change = 2% × 3.

∆ V / V = 2% × 3.

= (∆V)/(V) = 6% = 0.06%

Hence , Option (3) 0.06 is the right answer.

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Answer 2

Solutions :-

Given :
Percent change in length = 2%

Let side of cube be L
So, Volume = V = L³

Therefore,
$\frac{(ΔV)}{ ( V) }= 3 \frac {(ΔL)} { (L)}$

Percent Change in volume = 3 × percent change in length

So, Percent change in volume = 3 × 2%

$\frac{(ΔV)}{ (V) }= 3 \times 2 \% \\ \\ = > \frac{(ΔV)}{ (V) } = 6\% = 0.06$


The Bulk strain produced in it = 0.06

Hence,
Option (3) 0.06 is the required answer.