Question

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

• A. $\cos \theta$
• B. $\frac{2}{\cos \theta}$
• C. $\sqrt{5}$
• D. 1

Answer 1

Answer: (C)

As the bob is in equilibrium under the effect of three forces $-T, F$ and $W$

$\therefore T + P + W =0 $
From, the figure $ T \cos \theta=W\,\,\,...(i)$
$T \sin \theta=F\,\,\,...(ii)$
From Eqs. (i) and (ii)
$ T^{2} =W^{2}+F^{2} $
or $ T =\sqrt{W^{2}+F^{2}} $
$=\sqrt{(1)^{2}+(2)^{2}} $
$=\sqrt{5} $