Deformation of Bars due to Self Weight

Q. If all the dimensions of a prismatic bar of square cross-section suspended freely from the ceiling of a roof are doubled then the total elongation produced by its own weight will increase

1. eight times
2. four times
3. three times
4. two times

Q. A solid metal bar of uniform diameter D and length L is hang vertically from a ceiling. If the density of the material of the bar is $\rho$ and the modulus of elasticity is E, then the total elongation of the bar due to its own weight is

1. $\frac{\rho L}{2E}$
2. $\frac{\rho L^2}{2E}$
3. $\frac{\rho E}{2L}$
4. $\frac{\rho E}{2L^2}$

Q. A solid uniform metal bar of diameter D mm and length $lmm$ hangs vertically from its upper end, The density of the material is $pN/m{m}^3$ and its modulus of elasticity is $EN/m{m}^2$, The total extension of the rod due to its own weight would be

1. $\frac{\rho l^2}{2E}$
2. $\frac{\rho l}{2E}$
3. $\frac{\rho l}{4E}$
4. $\frac{\rho l^2}{4E}$