Two particles `A` and `B` each of mass `m` are kept stationary by applying a horizontal force `F = mg` on particle `B` as show in figure .Then

Options

A. `2tan beta=tan alpha`
B. `2T_(1)=5T_(2)`
C. `T_(1)sqrt(2)=T_(2)sqrt(5)`
D. None of these

Answer

C

Explanation

From fig, `T_(2) cos theta =mg, T_(2) sin theta = mg`

`T_(1) sin alpha = mg sqrt(2) sin 45^(@)`
`T_(1) sin alpha =mg implies (cos alpha)/(sin alpha) = (2mg)/(mg)`
`tan alpha = 1/2 implies cos alpha=(2)/(sqrt(5))`
`T_(1)(2)/(sqrt(5)) = 2mg implies T_(1)=mg sqrt(5)`
`(T_1)/(T_2) = (sqrt(5))/(sqrt(2)) implies sqrt(2)T_(1)=sqrt(5) T_(2)`.