As F < µMg , i.e. , rod is stationary so F = f where f is the friction force. Let Tis the tension in rod at distance x from the end where force has been applied.
Then, F - T - f1 = 0 & T = f2 Where f1+f2 = f = F As friction force is distributed uniformly, f1 =
fx
l
⇒ T = F - f1 = F -
f×x
l
= F [1−
x
l
] Let Δ(dx) be the elongation in dx length of rod, Δ(dx) =