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Longitudinal Strain

A rod of mass...

Question

A rod of mass $^{'} M^{'}$ is subjected to force $^{'} t^{'}$ and $^{'} 2 f^{'}$ at both the ends as shown in the figure. If young modulus of its material is $^{'} y^{'}$ and its length is $L$ find total elongation of rod.

\frac{f l}{2 A y}

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\frac{f l}{A y}

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\frac{3 f l}{2 A y}

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\frac{4 f l}{2 A y}

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Solution

The correct option is C $\frac{3 f l}{2 A y}$
To solve problem of these types we consider average force acting
$\begin{matrix} Δ l = \frac{F L}{A y} = (\frac{f_{1} + f_{2}}{2}) \frac{L}{A y} = (\frac{f + 2 f}{2}) \frac{L}{A y} = \frac{3 f L}{2 A y} T o t a l e l o n g a t i o n = Δ l = \frac{3 f L}{2 A y} H e n c e, t h e o p t i o n C i s t h e c o r r e c t a n s w e r . \end{matrix}$

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A rod of mass ′M′ is subjected to force ′t′ and ′2f′ at both the ends as shown in the figure. If young modulus of its material is ′y′ and its length is L find total elongation of rod.

The correct option is C 3fl2AyTo solve problem of these types we consider average force actingΔl=FLAy=(f1+f22)LAy=(f+2f2)LAy=3fL2AyTotalelongation=Δl=3fL2AyHence,theoptionCisthecorrectanswer.

A rod of mass $^{'} M^{'}$ is subjected to force $^{'} t^{'}$ and $^{'} 2 f^{'}$ at both the ends as shown in the figure. If young modulus of its material is $^{'} y^{'}$ and its length is $L$ find total elongation of rod.