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=30N`
Resolving the tension `T_(1)` into two mutually perpendicular components, we have
`T_(1)cos theta = T_(2)=30 N`
`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`