Question:
A mass of $10 \mathrm{~kg}$ is suspended by a rope of length $4 \mathrm{~m}$, from the ceiling. A force $\mathrm{F}$ 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 $g=10 \mathrm{~ms}^{-2}$ and the rope to be massless)
Correct Option: 1
Solution:
(1) From the free body diagram
$T \cos 45^{\circ}=100 \mathrm{~N}$
$T \sin 45^{\circ}=F$
On dividing (i) by (ii) we get
$\frac{T \cos 45^{\circ}}{T \sin 45^{\circ}}=\frac{100}{F}$
$\Rightarrow \quad F=100 \mathrm{~N}$