Question

A uniform rod is kept on a smooth horizontal surface, a constant force is applied on the rod in horizontal direction at end 'A'. Find the ratio of energy stored per unit volume at end A to the energy stored per unit volume in the middle of the rod.

• A. 2
• B. 4
• C. 8
• D. 6

Answer 1

The correct option is B 4

$U=\frac{1}{2}\frac{(stress{)}^2}{Y}$
$Stress=\frac{Tension}{area}$
$\frac{U_A}{U_{middle}}=\frac{T_A^2}{(T_{middle}{)}^2}$


Since the surface is smooth, let the rod move with acceleration $a$
From the FBD of the rod,
$T_A=F=Ma$
$T_{middle}=\frac{M}{2}a=\frac{F}{2}$

$\therefore \frac{U_A}{U_{middle}}=\frac{F^2}{(\frac{F}{2}{)}^2}=4$