ltbrltgt A string of mass m (can be non uniform as well) is suspended through two points which are not in same horizontal level. Tension in the string at the end points are `T_(1)` and `T_(2)` and at the lowest point is `T_(3)`. Mass of string in terms of `T_(1),T_(2)` and `T_(3)` can be represented a (uniform gravity 'g' exists downwards)

Options

A. `(sqrt(T_(1)^(2)-T_(3)^(2))+sqrt(T_(2)^(2)-T_(3)^(2)))/(g)`
B. `((T_(1)+T_(2)-2T_(3)))/(g)`
C. `(sqrt(T_(1)^(2)+T_(2)^(2)))/(g)`
D. `(sqrt(T_(1)^(2)+T_(3)^(2))+sqrt(T_(2)^(2)+T_(3)^(2)))/(g)`

Answer

A

Explanation

`T_(1)cosalpha=T_(3)=T_(2)cosbeta`
`T_(1)sinalpha+T_(2)sinbeta=mg`
`impliesmg=T_(1)sqrt(1-((T_(3))/(T_(1)))^(2))+T_(2)sqrt(1-((T_(3))/(T_(2)))^(2))`
`impliesm=(sqrt(T_(1)^(2)+T_(3)^(2))+sqrt(T_(2)^(2)-T_(3)^(2)))/(g)`