Question

A mass of $10 \,kg$ is suspended vertically by a rope of length $5\, m$ from the roof. A force of $30\, N$ is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $\theta=\tan ^{-1}\left(x \times 10^{-1}\right)$. The value of $x$ is _____.
(Given $\left.g=10 \,m / s ^{2}\right)$

Answer 1

$T \sin \theta=30$
$T \cos \theta=100$
$\Rightarrow \tan \theta=0.3$