Question

A uniform cube is subjected to volume compression. If each side is deceased by 3%,
A. $27\%$
B. $8\%$
C. $9\%$
D. $1\%$

Answer 1

Hint:To resolve this problem, students need to know about bulk strain definition and formulation and the formulation for density. With the general equation of bulk pressure, we are able to find the answer to this problem. Volumetric strain or bulk strain is described as the change in volume per unit of original volume. When the body is deformed through outside forces.

Formula Based:
Volumetric strain $=\dfrac{\text{change in volume}}{\text{original volume}}=\dfrac{\Delta V}{V}$

Complete step by step solution:
Let the initial volume be $V$and the change in volume (final volume) be $\Delta V$.
We know that, the volume of cube $(V)={{a}^{3}}$
So, Change in volume = Change in length
We have given that the length is decreased by $3\%$.
By using error percentage error formula we get,
$\%\text{ change in volume =3}\times \text{ change in length} \\
\dfrac{\Delta V}{V}=3\times \dfrac{\Delta a}{a}\cdots \cdots (1) \\ $
As each side is decreased by $3\%$ therefore $\dfrac{\Delta a}{a}=1%$
Substituting the above relation in equation (1), we get
$\Rightarrow \dfrac{\Delta V}{V}=3\times 3\% \\
\therefore \dfrac{\Delta V}{V}=9\% $
Hence, change in bulk strain is $9\%$.

Hence, the correct option is C.

Additional information:
Tangential or shear stress: When the direction of the deforming force or outside pressure is parallel to the cross-sectional area, the stress experienced through the object is known as shearing stress or tangential stress.

Volume stress or Bulk stress: When normal stress modifications the volume of a body then it is called volume strain.
$Volume\text{ Stress =}\dfrac{Force}{Area}$

Longitudinal stress: When an object is one dimensional then force performing per unit area is called longitudinal stress.

Longitudinal strain: It is defined as the increase in the length per unit original length, when the body is deformed by outside force.

Note: We have taken three instances of the alternate in duration from the equation of percent error. We should remember that we have to measure the bulk strain in percentage. To solve this question, we know about the volumetric strain and its formula.