Question

A mass of $10\text{kg}$ is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle ${45}^{\circ }$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ($g=10{\text{ms}}^{-2}$)

• A. $\text{200 N}$
• B. $\text{140 N}$
• C. $\text{70 N}$
• D. $\text{100 N}$

Answer 1

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

Freebody diagram of the problem is draw as


At equilibrium,

$\tan {45}^{\circ }=\frac{mg}{F}=\frac{100}{F}$

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

Hence, $\left(D\right)$ is the correct answer.