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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


1. 2 times
2. 4 times
3. 8 times
4. 10 times

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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.

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