A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $45 ^ { \circ }$ with the vertical. Then F equals: (Take $\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ and the rope to be massless)\\
(1) 100 N\\
(2) 90 N\\
(3) 70 N\\
(4) 75 N