Question

a string of lenght l and mass m is lying on a horizontal table. a force f is applied at one of its end.tension on the string at a distance y from the end at which the fprce applied is ?

Answer 1

mass per unit length = rho = (m/L)

this is exactly like a rope hanging from a hook. The tension is zero at the bottom and m g at the top just below the hook. Here g is replaced with a
where
a = F/m
so the tension is
T = rho (L-y) a
or
T = (m/L) (L-y) (F/m)
T = (1-Y/L)F