A cube is subjected to a uniform volume.compression, if the side of the cube decreases by 1% the bulk strain is

Options

A. 0.01
B. 0.02
C. 0.03
D. 0.06

Answer

C

Explanation

Let L be the length of each side of the cube, Initial volume =`L^(3)`
When each side decreases by 1% new length
`L. = L - (L)/(100) = (99L)/(100)`
New volume `= L.^(3) = ((99L)/(100))^(3)`
Change in volume, `Delta V= L^(3) - ((99L)/(100))^(3)`
or `Delta V= L^(3) [1- (1- (1)/(100))^(3)]`
`= L^(3) [1- (1- (3)/(100) + ...)] = L^(3) [(3)/(100)] = (3L^(3))/(100)` [neglecting higher order term]
`:.` Bulk strain `= (Delta V)/(V) = (3L^(3)//100)/(L^(3)) = 0.03`