First slide

Different types of Forces

Question

A homogeneous rod of length ‘L’ is acted upon by two forces F₁ and F₂ applied to its ends and directed opposite to each other. If F₂ > F₁, then with what force ‘F’ will the rod be stretched at the cross-section at a distance l from the end where F₁ is applied

Moderate

A

$\large \frac{{({F_2} - {F_1})l}}{L}$
B

$\large \frac{{({F_2} - {F_1})l}}{L}+F_1$
C

$\large \frac{{({F_2} + {F_1})l}}{2L}$
D

$\large \frac{{(F_{_2}^2 - F_{_1}^2)l}}{L}$

Solution

$\large a = \frac{{{F_2} - {F_1}}}{M} \Rightarrow T - {F_1} = \left( {\frac{{{F_2} - {F_1}}}{{\cancel{M}}}} \right)\frac{{\cancel{{\rm M}}}}{L}\ell$
$\large T = {F_1} + \left( {\frac{{{F_2} - {F_1}}}{L}} \right)\ell$

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