A uniform cube is subjected to volume compression. If each side is decreased by 1 % then 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 cube, then initial volume `= L^(3)`. When each side decreases by 1%. Then new length, `L' = L - (1)/(100) = (99 L)/(100)`
New volume `= L^(3) - ((99L)/(100))^(3)`
`:.` change in volume
`Delta V = L^(3) - ((99L)/(100))^(3)`
`= L^(3) [1 - (1 - (3)/(100) + ..)] = L^(3) [(3)/(100)] = (3L^(3))/(100)`
`:.` Bulk strain `= (Delta V)/(V) = (3 L^(3) // 100)/(L^(3)) = 0.03`