A mass of 3kg is suspended by a rope of length 2m from the ceiling. A force of 40N in the' horizontal direction is applied at midpoint P of the rope as shown. What is the angle the rope makes with the vertical in equilibrium and the tension in part of string attached to the ceiling ? (Neglect the mass of the rope, `g = 10m//s^2`)

Explanation

In equilibrium `T_(2) =W = 30 N`
Resolving the tension `T_(1)` into two mutually perpendicular components, we have
`T_(1) cos_(x) = T_(2) = 30 N rArr T_(1)sin theta = 40 N`
`tan theta = 4/3 rArr theta = 53^(@)`
The tension in part of string attached to the ceiling
`T_(1) = sqrt(W^(2) + F^(2)) = sqrt(30^(2) + 40^(2) N) = 50 N`