Question

Question #2546b

Answer 1

See below

Explanation:

The question only makes sense if we take into account the mass of the string.

The small element `dx` will have mass: `dm= M/L dx`, assuming the string is of uniform density.

The FBD for the small element requires:

`sum mathbf F = m mathbf a`

`implies T + dT - T = dm \ a`

`implies dT = M/L dx \ a`

`implies T = M/L a x + C`

`T(0) = 10 implies C = 10`

`T(L) = 20 implies 20 = M/La L + 10`

`implies T = 10/L x + 10`

Which is simply a linear increase along the string which is what intuitively one would expect.