A cube is subjected to a uniform volume compression from all side. If the side of the cube decreases by 1%, the bulk strain `((Delta V)/(V))` is ……

Options

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

Answer

C

Explanation

Let L be each side of the cube and its volume `V = L ^(3)`
When each side length decreases by ` % `then new length,
L. = L - L ` of `1%`
`= L -0.91 L = 0.99 L`
`therefore` New volume `V. = (0.99 L) ^(3)`
`therefore ` Change in volume `Delta V =V - V.`
`= L ^(3) - (0.99L)^(3)`
`=L^(3) [1- 0.99]^(3)`
`=L^(3) [1- (1-0.01)^(3)]`
`=L^(3)[1-(1-0.03+...)]`
[Neglecting terms having higher power in expansion]
`=L ^(3) [0.03]`
`therefore (Delta V )/(V) = ( L ^(3) xx 0.03)/(L ^(3))`
`therefore `Bulk strain `= 0.03`