Correct Answer - Option 3 : 8 times
Concept:
For a cantilever beam of length 'l' and carrying a point load 'P' at the free end. The slope and deflection at the free end are given by:
\(\theta=\frac{Pl^2}{2EI}\;\;and\;\;\Delta=\frac{Pl^3}{3EI}\)
Calculation:
Given:
P1 = 2P, L = 2L, I = 2I
\(\Delta_1=\frac{2P(2l)^3}{3E(2I)} = \frac{8Pl^3}{3EI} = 8\Delta\)
So, If the concentrated load applied at the free end of a cantilever beam is doubled along with its length and moment of inertia also, then the deflection at the free end will increase by 8 times.