Question

c) W
5. Four identical metal butterflies are hanging from a li
string of length 51 at equally placed points as shown.TW
ends of the string are attached to a horizontal fixed support
The middle section of the string is horizontal. The relati
between the angle, and is given by
(a) sin 8, = 2 sin a
(b) 2 cos , = sin
U tan 8, = 2 tan
(d) < , and no other conclusion can be derived​

Answer 1

Answer:

Taking the position to be A,B C and D from first to last.

For knot A we have T1sinx1 = mg +T2sinx2 and again T1cosx1= T2cosx2 we get the angles by taking FBD of point A.

For knot B T2sinx2 = mg.

Now on solving first equation we have T1sinx1=(mg + mg)= 2mg.

And then T2sinx2/T1sinx1 = mg /2mg or T2/T1 = sinx1 / 2sinx2.

Again, T2/T1 = cosx2/cosx1 hence on comparing cosx2/cosx1 =sinx1 / 2sinx2 we get than tanx1 = 2tanx2.