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 ……

A cube is subjected to a uniform volume compression from all side. If

1.	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 ……
Answer» `0.01` `0.02` `0.03 `0.06` SOLUTION :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`