Question 194: Laws of Motion

Question

The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, angle $	heta$ should be
![](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1m4rufy1u/96d132ee-edd0-4251-a2a3-0ddbc32b8546/7bf6b020-bc1e-11ef-a3b7-5fce4990f0b5/file-jaoe38c1m4rufy1v.png?format=png)

Accepted Answer

From the diagram,
$\mathrm{T}=\mathrm{Mg}$ and,
For the system to remain in equilibrium,
$\begin{array}{ll} 
& 2 \mathrm{~T} \cos 	heta=\sqrt{2} \mathrm{Mg} \
	herefore & 2 \mathrm{~T} \cos 	heta=\mathrm{T} \sqrt{2} \
	herefore & \cos 	heta=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}} \
	herefore & \quad 	heta=\cos ^{-1}\left(\frac{1}{\sqrt{2}}ight)
\end{array}$
![](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1m4ruh3e9/0ab4ac89-c778-45e3-92f3-76e629259129/9be6ce10-bc1e-11ef-a3b7-5fce4990f0b5/file-jaoe38c1m4ruh3ea.png?format=png)

Answer

$\cos ^{-1}(1)$

Answer

$\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Answer

$\cos ^{-1}\left(\frac{1}{2}\right)$

Answer

$\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)$

Laws of Motion

The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, angle \theta should be

Choose the correct answer: