A mass of 10   k g is suspended by a rope of length 4   m , from the ceiling. A force F is applied…

Let the tension in the string is $T$.

Applying the condition of equilibrium in the vertical direction,

$T\cos \left(45°\right)=100$

$\Rightarrow \frac{T}{\sqrt{2}}=100$   $...\left(1\right)$

In the horizontal direction,

$T\sin \left(45°\right)=F$

$\Rightarrow \frac{T}{\sqrt{2}}=\mathrm{F}$

Put the value of $T$ from equation $\left(1\right)$,

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

So, the horizontal force applied on the rope will be $100 \mathrm{N}$.