A $1 \mathrm{~N}$ pendulum bob is held at an angle $\theta$ from the vertical by a $2 \mathrm{~N}$ horizontal force $\mathrm{F}$ as shown in the figure. The tension in the string supporting the pendulum bob (in newton) is

• A

  $\cos \theta$
• B

  $\frac{2}{\cos \theta}$
• Correct answer
  C

  $\sqrt{5}$
• D

  1

Solution

As the bob is in equilibrium under the effect of three forces $-T, F$ and $W$
$\therefore \quad \mathbf{T}+\mathbf{P}+\mathbf{W}=0$
From Eqs. (i) and (ii) $T^2=W^2+F^2$ $\text { or } \quad \begin{aligned} T & =\sqrt{W^2+F^2} \\ & =\sqrt{(1)^2+(2)^2} \\ & =\sqrt{5} \end{aligned}$

Hence, the correct answer is option: 'C'.