Laws Of Motion Question 317
Question: A weight W is supported by two cables as shown. The tension in the cable making angle $ \theta $ with horizontal will be the minimum when the value of $ \theta $ is.
Options:
A) 0
B) $ 30{}^\circ $
C) $ 60{}^\circ $
D) $ 45{}^\circ $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ T _{2}\sin \theta +T _{1}\sin 60{}^\circ =W $
$ T _{1}\cos 60{}^\circ =T _{2}\cos \theta $
$ T _{2}\sin \theta +T _{2}\cos \theta .\tan 60{}^\circ =W $
$ T _{2}(\sin \theta +\sqrt{3}\cos \theta )=W $
$ 2T _{2}(\sin 30{}^\circ \sin \theta +\cos 30{}^\circ \cos \theta )=W $
$ \cos ( 30{}^\circ -\theta)\text{ is maximum} $
$ \text{If }30{}^\circ -\theta =0;\theta =30{}^\circ $
