Answer:
20 m/s
Explanation:
The speed of a wave is given by:
![v=\lambda f](https://tex.z-dn.net/?f=v%3D%5Clambda%20f)
where
is the wavelength
f is the frequency
v is the speed
For the wave in this problem,
f = 10 Hz is the frequency
is the wavelength
So the speed is
![v=(10 Hz)(2 m)=20 m/s](https://tex.z-dn.net/?f=v%3D%2810%20Hz%29%282%20m%29%3D20%20m%2Fs)
Answer:
Charge on each metal sphere will be ![8\times 10^{8}C](https://tex.z-dn.net/?f=8%5Ctimes%2010%5E%7B8%7DC)
Explanation:
We have given number of electron added to metal sphere A ![n=10^{12}electron](https://tex.z-dn.net/?f=n%3D10%5E%7B12%7Delectron)
As both the spheres are connected by rod so half -half electron will be distributed on both the spheres.
So electron on both the spheres ![=\frac{10^{12}}{2}=5\times 10^{11}electron](https://tex.z-dn.net/?f=%3D%5Cfrac%7B10%5E%7B12%7D%7D%7B2%7D%3D5%5Ctimes%2010%5E%7B11%7Delectron)
We know that charge on each electron ![e=1.6\times 10^{-19}C](https://tex.z-dn.net/?f=e%3D1.6%5Ctimes%2010%5E%7B-19%7DC)
So charge on both the spheres will be equal to ![q=1.6\times 10^{-19}\times 5\times 10^{11}=8\times 10^{8}C](https://tex.z-dn.net/?f=q%3D1.6%5Ctimes%2010%5E%7B-19%7D%5Ctimes%205%5Ctimes%2010%5E%7B11%7D%3D8%5Ctimes%2010%5E%7B8%7DC)
So charge on each metal sphere will be equal to ![8\times 10^{8}C](https://tex.z-dn.net/?f=8%5Ctimes%2010%5E%7B8%7DC)
<span>4.5 m/s
This is an exercise in centripetal force. The formula is
F = mv^2/r
where
m = mass
v = velocity
r = radius
Now to add a little extra twist to the fun, we're swinging in a vertical plane so gravity comes into effect. At the bottom of the swing, the force experienced is the F above plus the acceleration due to gravity, and at the top of the swing, the force experienced is the F above minus the acceleration due to gravity. I will assume you're capable of changing the velocity of the ball quickly so you don't break the string at the bottom of the loop.
Let's determine the force we get from gravity.
0.34 kg * 9.8 m/s^2 = 3.332 kg m/s^2 = 3.332 N
Since we're getting some help from gravity, the force that will break the string is 9.9 N + 3.332 N = 13.232 N
Plug known values into formula.
F = mv^2/r
13.232 kg m/s^2 = 0.34 kg V^2 / 0.52 m
6.88064 kg m^2/s^2 = 0.34 kg V^2
20.23717647 m^2/s^2 = V^2
4.498574938 m/s = V
Rounding to 2 significant figures gives 4.5 m/s
The actual obtainable velocity is likely to be much lower. You may handle 13.232 N at the top of the swing where gravity is helping to keep you from breaking the string, but at the bottom of the swing, you can only handle 6.568 N where gravity is working against you, making the string easier to break.</span>