Question

A mass of $10\text{kg}$ is suspended by a rope of length $4\text{m}$, 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 $g=10{\text{ms}}^{-2}$ and the rope to be massless)

• A. $100\text{N}$
• B. $90\text{N}$
• C. $70\text{N}$
• D. $75\text{N}$

Answer 1

The correct option is A $100\text{N}$


In equilibrium, at point $O$,

In vertical direction,

$T\cos {45}^{\circ }=100\text{N}\dots \left(i\right)$

In horizontal direction,

$T\sin {45}^{\circ }=F\dots \left(ii\right)$

On dividing $\left(i\right)$ by $\left(ii\right)$

$\frac{T\cos {45}^{\circ }}{T\sin {45}^{\circ }}=\frac{100}{F}$

$\Rightarrow F=100\text{N}$

Hence, option $\left(\text{A}\right)$ is correct.