Figure-2.107 shows a block of mass m attached to a spring of force constant k and connected to ground by two string of equal lengths making an angle `90^(@)` with each other. In relaxed state natural length of the spring is l. In the situation shown in figure, find the tensions in the two strings.

Options

A. `T_(1) = sqrt3 ((kl)/(4) - (mg)/(2)) , T_(2) = (kl)/(4) - (mg)/(2)`
B. `T_(1) = sqrt3((kl)/(4) + (mg)/(2)) , T_(2) = (kl)/(4) - (mg)/(2)`
C. `T_(1) = (kl)/(4) - (mg)/(2) , T_(2) = sqrt3 ((kl)/(4) + (mg)/(2))`
D. `T_(1) = (kl)/(4) - (mg)/(2) , T_(2) = sqrt3 ((kl)/(4) - (mg)/(2))`

Answer

A

Explanation

`T_(1) = sqrt3 T_(2)` ……(1)
`(kl)/(2) = mg + T_(1) (sqrt3)/(2) + (T_(2))/(2)` … (2)
Solving (1) & (2) to get,
`T_(1) = sqrt(3((kl)/(4) - (mg)/(2))` & `T_(2) = (kl)/(4) - (mg)/(2)`