Answer:
Yes the frequency of the angular simple harmonic motion (SHM) of the balance wheel increases three times if the dimensions of the balance wheel reduced to one-third of original dimensions.
Explanation:
Considering the complete question attached in figure below.
Time period for balance wheel is:
![T=2\pi\sqrt{\frac{I}{K}}](https://tex.z-dn.net/?f=T%3D2%5Cpi%5Csqrt%7B%5Cfrac%7BI%7D%7BK%7D%7D)
![I=mR^{2}](https://tex.z-dn.net/?f=I%3DmR%5E%7B2%7D)
m = mass of balance wheel
R = radius of balance wheel.
Angular frequency is related to Time period as:
![\omega=\frac{2\pi}{T}\\\omega=\sqrt{\frac{K}{I}} \\\omega=\sqrt{\frac{K}{mR^{2}}](https://tex.z-dn.net/?f=%5Comega%3D%5Cfrac%7B2%5Cpi%7D%7BT%7D%5C%5C%5Comega%3D%5Csqrt%7B%5Cfrac%7BK%7D%7BI%7D%7D%20%5C%5C%5Comega%3D%5Csqrt%7B%5Cfrac%7BK%7D%7BmR%5E%7B2%7D%7D)
As dimensions of new balance wheel are one-third of their original values
![R_{new}=\frac{R}{3}](https://tex.z-dn.net/?f=R_%7Bnew%7D%3D%5Cfrac%7BR%7D%7B3%7D)
![\omega_{new}=\sqrt{\frac{K}{mR_{new}^{2}}}\\\\\omega_{new}=\sqrt{\frac{K}{m(\frac{R}{3})^{2}}}\\\\\omega_{new}={3}\sqrt{\frac{K}{mR^{2}}}\\\\\omega_{new}={3}\omega](https://tex.z-dn.net/?f=%5Comega_%7Bnew%7D%3D%5Csqrt%7B%5Cfrac%7BK%7D%7BmR_%7Bnew%7D%5E%7B2%7D%7D%7D%5C%5C%5C%5C%5Comega_%7Bnew%7D%3D%5Csqrt%7B%5Cfrac%7BK%7D%7Bm%28%5Cfrac%7BR%7D%7B3%7D%29%5E%7B2%7D%7D%7D%5C%5C%5C%5C%5Comega_%7Bnew%7D%3D%7B3%7D%5Csqrt%7B%5Cfrac%7BK%7D%7BmR%5E%7B2%7D%7D%7D%5C%5C%5C%5C%5Comega_%7Bnew%7D%3D%7B3%7D%5Comega)
Answer:
yes ,what's the question
and if the question is why
then it's for gravity
The answer is in the attachment
<span>...........................................</span>
Answer:
![2.1\times 10^{-12} c](https://tex.z-dn.net/?f=2.1%5Ctimes%2010%5E%7B-12%7D%20c)
Explanation:
We are given that
Surface area of membrane=![5.3\times 10^{-9} m^2](https://tex.z-dn.net/?f=5.3%5Ctimes%2010%5E%7B-9%7D%20m%5E2)
Thickness of membrane=![1.1\times 10^{-8} m](https://tex.z-dn.net/?f=1.1%5Ctimes%2010%5E%7B-8%7D%20m)
Assume that membrane behave like a parallel plate capacitor.
Dielectric constant=5.9
Potential difference between surfaces=85.9 mV
We have to find the charge resides on the outer surface of membrane.
Capacitance between parallel plate capacitor is given by
![C=\frac{k\epsilon_0 A}{d}](https://tex.z-dn.net/?f=C%3D%5Cfrac%7Bk%5Cepsilon_0%20A%7D%7Bd%7D)
Substitute the values then we get
Capacitance between parallel plate capacitor=![\frac{5.9\times 8.85\times 10^{-12}\times 5.3\times 10^{-9}}{1.1\times 10^{-8}}](https://tex.z-dn.net/?f=%5Cfrac%7B5.9%5Ctimes%208.85%5Ctimes%2010%5E%7B-12%7D%5Ctimes%205.3%5Ctimes%2010%5E%7B-9%7D%7D%7B1.1%5Ctimes%2010%5E%7B-8%7D%7D)
![C=0.25\times 10^{-12}F](https://tex.z-dn.net/?f=C%3D0.25%5Ctimes%2010%5E%7B-12%7DF)
V=![85.9 mV=85.9\times 10^{-3}](https://tex.z-dn.net/?f=85.9%20mV%3D85.9%5Ctimes%2010%5E%7B-3%7D)
![Q=CV](https://tex.z-dn.net/?f=Q%3DCV)
![Q=0.25\times 10^{-12}\times 85.9\times 10^{3}=2.1\times 10^{-12} c](https://tex.z-dn.net/?f=Q%3D0.25%5Ctimes%2010%5E%7B-12%7D%5Ctimes%2085.9%5Ctimes%2010%5E%7B3%7D%3D2.1%5Ctimes%2010%5E%7B-12%7D%20c)
Hence, the charge resides on the outer surface=![2.1\times 10^{-12} c](https://tex.z-dn.net/?f=2.1%5Ctimes%2010%5E%7B-12%7D%20c)
A hypothesis is a tentative statement which is made to try to explain a known phenomenon but whose truth value is still uncertain, whether it is true or no depends on further research. On the other hand, a theory is made up of hypothesis which have been proven to be true so far, a theory should be able to explain future phenomena successfully