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If a rod of length $l$ , very small area of cross section A, Young’s modulus of Elasticity Y is acted upon by parallel forces 3F and F respectively as shown in fig. Within elastic limit to study change in length of the rod $(Δ l)$ and its elastic potential energy (U) the rod in segmented into four equal parts where magnitude of change in lengths are $Δ l_{1}$ , $Δ l_{2}$ , $Δ l_{3}$ , $Δ l_{4}$ and elastic potential energy stored in each segment are $U_{1}, U_{2}, U_{3}, U_{4}$ respectively as shown then which is /are correct.

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$U_{1} = U_{2} < U_{3} < U_{4}$

$Δ l_{2} = \frac{Δ l_{4}}{5} = \frac{Δ l}{8}$

$U_{1} < \frac{U}{4} < U_{4}$

$Δ l_{1} = \frac{Δ l_{3}}{3} = \frac{Δ l}{8}$

answer is A, B, C, D.

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Detailed Solution

Energy stored in a strained rod = $\frac{1}{2} s t r e s s \times s t r a i n$ .

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