A $1 \mathrm{~N}$ pendulum bob is held at an angle $\theta$ from the vertical by a $2 \mathrm{~N}$…
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
$\cos \theta$
$\frac{2}{\cos \theta}$
$\sqrt{5}$
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)
$T^2=W^2+F^2$
$\text { or } \quad \begin{aligned}
T & =\sqrt{W^2+F^2} \\
& =\sqrt{(1)^2+(2)^2} \\
& =\sqrt{5}
\end{aligned}$
