Ah, i get it now! The first equation should have had ##a_y## and the second, ##a_x## (i did it by mistake). And the 3rd equation should have been:
$$ T \sin \theta \cdot \frac l2 = \frac{ml^2}{12} \cdot \alpha \qquad \text{...(iii)} $$
Now the answer comes as:
$$ T=\frac{mg}{4 \sin \theta +...
Homework Statement
"Find the tension in the right string, when the left string is cut, if the mass of the rod is ##m## and its length is ##l##, and ##\sin \theta = 3/5##. The rod is initially horizontal." Please refer the diagram below (sorry for its clumsiness!).
Homework Equations
$$I_{rod}...
If you mean that the book says ##\large \theta = \cos^{-1}\left(\frac {\sqrt 3}{3}\right)##, then it is the same as ##\large \theta = \cos^{-1}\left(\frac {1}{\sqrt 3}\right)##! Your answer is correct! :)
Also, I see that perhaps my doubt #3 is a bit confusing. So I will reword it:
1. Standing waves on string fixed at both ends
Consider a wave ##y_i = y_0 \sin(kx - \omega t)## on a string fixed at ##x=0## and ##x=L##.
As the incident wave gets reflected from the fixed end at ##x=L##, the...
Thanks for the detailed answer, but I already knew this explanation from our textbook! What I further need is how do we explain this in terms of forces only [this is for doubt (1)]. I now realize that maybe this delves deep into how a wave actually propagates on a string in terms of forces...!
Most interesting parts of physics for me is mechanics and energy. However like most others, I also immensely like Cosmic Physics and Quantum Physics for reading sometimes! :)
I have three doubts in regard to waves on a string which I will try to make as clear as possible.
For this purpose, I have considered a general wave:
$$y_i=y_0\sin(\omega t - kx)$$
(1) If a wave pulse:
$$y = y_0 e^{\frac{-1}{T^2} \left(t-\frac xv \right)^2}$$
is incident against a rigid...
Homework Statement
[/B]
"Derive a relation between the static pressure P at a point and its depth y from the free surface of the liquid. Given the surface density of liquid is ρο, and compressibility of the liquid is k."
Homework Equations
##ρ(P) = ρ_οe^{kP}##
##dP = ρg dy##
The Attempt at a...
Hello! I am introducing myself here. I am a student studying class 11 and a physics enthusiast! I especially love practical applications of physics. Thanks for "reading" me out! :smile: