Question

A 1 kg mass is suspended from the ceiling by a rope of length 4m. A horizontal force 'F' is applied at the mid point of the rope so that the rope makes an angle of 45° with respect to the vertical axis as shown in figure. The magnitude of F is : 

 

(1) \(\frac{10}{\sqrt{2}} \mathrm{N}\)

(2) \(1 \mathrm{~N}\)

(3) \(\frac{1}{10 \times \sqrt{2}} \mathrm{N}\)

(4) \(10 \mathrm{~N}\)

Answer 1

Correct option is :  (4) \(10 \mathrm{~N}\) 

 

From figure

AS system is in equilibrium, therefore 

\( \begin{aligned} & \mathrm{T}_1 \cos 45^{\circ}=\mathrm{mg} \end{aligned} \) 

\( \begin{aligned} \mathrm{T}_1 \sin 45^{\circ}=\mathrm{F} \end{aligned} \) 

\( \begin{aligned} \therefore \tan 45^{\circ}=\frac{\mathrm{F}}{\mathrm{mg}} \end{aligned} \) 

\( \begin{aligned} \Rightarrow \mathrm{F}=\mathrm{mg} \end{aligned} \) 

\(\text{F}= 10 \ \text{N}\)