A mass of `4kg` is suspended by a rope of length `4m` from a ceiling. A force of `20N` in the horizontal direction is applied at the mid-point of the rope as shown in figure. What is the angle which the rope makes with the vertical in equilibrium? Neglect the mass of the rope. Take `g=10ms^(-2)` .

Options

A. `tan^(-1)2`
B. `tan^(-1)((1)/(2))`
C. `tan^(-1)sqrt(2)`
D. `tan^(-1)(1)(sqrt2)`

Answer

B

Explanation

`T_(2)=mg=4xx10=40N`
`T_(1)costheta=40` , `T_(1)sintheta=20`
`tantheta=(1)/(2)` implies `theta=tan^(-1)((1)/(2))` .