A light rod with uniform cross-section of `10^(-4)m^(2)` is shown in the figure. The rod consists of three different materials whose lengths are 0.1 m, 0.2 mand 0.15 m respectively and whose Young's moduli are `2.5 xx 10^(10) N//m^(2), 4xx10^(10) N//m^(2)` and `1 xx 10^(10) N//m^(2)` respectively. The displacement of point B will be

Options

A. `24xx10^(-6) ` m
B. `9 xx 10^(-6)` m
C. `4 xx 10^(-6) m`
D. `1xx10^(-6) m`

Answer

C

Explanation

Increment in the length AB =`(MgL)/(AY) = (10xx 10xx0.1)/(10^(-4) xx 2.5 xx 10^(10)) = 4xx 10^(-6)` m
`:.` Displacement of point `B = 4 xx 10^(-6)` m