A prismatic linearly elastic bar of length $L,$ cross-sectional area $A,$ and made up of a material with Young's modulus $E,$ is subjected to axial tensile force as shown in the figures. When the bar is subjected to axial tensile forces $P_{1}$ and $P_{2}$, the strain energies stored in the bar are $U_{1}$ and $U_{2},$ respectively.

If $U$ is the strain energy stored in the same bar when subjected to an axial tensile force $\left(P_{1}+P_{2}\right),$ the correct relationship is

(A) $U=U_{1}+U_{2}$

(B) $U=U_{1}-U_{2}$

(C) $U (D) $U>U_{1}+U_{2}$

A prismatic linearly elastic bar of length $L,$ cross-sectional area $A,$ and made up of a material with Young's modulus $E,$ is subjected to axial tensile force as shown in the figures. When the bar is subjected to axial tensile forces $P_{1}$ and $P_{2}$, the strain energies stored in the bar are $U_{1}$ and $U_{2},$ respectively.

If $U$ is the strain energy stored in the same bar when subjected to an axial tensile force $\left(P_{1}+P_{2}\right),$ the correct relationship is

(A) $U=U_{1}+U_{2}$

(B) $U=U_{1}-U_{2}$

(C) $U (D) $U>U_{1}+U_{2}$

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