Question

A rubber ball of radius R was compressed by a force and the ball shrinks by a radius R/4. What is the volume strain on the ball:

• A. 1/16
• B. 5/16
• C. 37/64
• D. 9/16

Answer 1

Answer: (C)

37/64

Given : A rubber ball of radius R was compressed by a force and the ball shrinks by a radius R/4. What is the volume strain on the ball:

Solution :

Volume strain = $\frac{\Delta V}{V}$ = $\frac{V_i-V_f}{V_i}$ = $1-\frac{V_f}{V_i}$ eq-1

Initial radius = R , final radius = $\frac{3R}{4}$ as it shrinks by $\frac{r}{4}$

$V_i=\frac{4}{3}\pi R^3$ and $V_f=\frac{4}{3}\pi R^3\frac{27}{64}$

Substituting the values in eq-1 we get

Volume Strain = $1-\frac{27}{64}$ = $\frac{37}{64}$