Answer:
when u think about that the answer is gone be d thats my answer D
Explanation:
Absolutely not. You can have a piece of wood and water with the same dimensions, but dimensions Won't matter
Answer:
Part a)
![v = 6.4 \times 10^3 m/s](https://tex.z-dn.net/?f=v%20%3D%206.4%20%5Ctimes%2010%5E3%20m%2Fs)
Part b)
![v = 2.44 \times 10^4 m/s](https://tex.z-dn.net/?f=v%20%3D%202.44%20%5Ctimes%2010%5E4%20m%2Fs)
Explanation:
Magnetic field due to outer solenoid inside it is given as
![B_1 = \mu_0 \frac{N}{L} i](https://tex.z-dn.net/?f=B_1%20%3D%20%5Cmu_0%20%5Cfrac%7BN%7D%7BL%7D%20i)
![B_1 = (4\pi \times 10^{-7})(\frac{545}{0.205})(4.53)](https://tex.z-dn.net/?f=B_1%20%3D%20%284%5Cpi%20%5Ctimes%2010%5E%7B-7%7D%29%28%5Cfrac%7B545%7D%7B0.205%7D%29%284.53%29)
![B_1 = 0.015 T](https://tex.z-dn.net/?f=B_1%20%3D%200.015%20T)
Now similarly we have
magnetic field due to inner solenoid on it axis is given as
![B_2 = \mu_0 \frac{N}{L} i](https://tex.z-dn.net/?f=B_2%20%3D%20%5Cmu_0%20%5Cfrac%7BN%7D%7BL%7D%20i)
![B_2 = (4\pi \times 10^{-7})(\frac{331}{0.189})(1.49)](https://tex.z-dn.net/?f=B_2%20%3D%20%284%5Cpi%20%5Ctimes%2010%5E%7B-7%7D%29%28%5Cfrac%7B331%7D%7B0.189%7D%29%281.49%29)
![B_2 = 3.28\times 10^{-3} T](https://tex.z-dn.net/?f=B_2%20%3D%203.28%5Ctimes%2010%5E%7B-3%7D%20T)
Part a)
Now if a proton is revolving around the common axis of two solenoids
then we will have
![qv(B_1 - B_2) = \frac{mv^2}{R}](https://tex.z-dn.net/?f=qv%28B_1%20-%20B_2%29%20%3D%20%5Cfrac%7Bmv%5E2%7D%7BR%7D)
![(1.6 \times 10^{-19})(15 - 3.28)\times 10^{-3} = \frac{1.66\times 10^{-27} v}{5.69 \times 10^{-3}}](https://tex.z-dn.net/?f=%281.6%20%5Ctimes%2010%5E%7B-19%7D%29%2815%20-%203.28%29%5Ctimes%2010%5E%7B-3%7D%20%3D%20%5Cfrac%7B1.66%5Ctimes%2010%5E%7B-27%7D%20v%7D%7B5.69%20%5Ctimes%2010%5E%7B-3%7D%7D)
![v = 6.4 \times 10^3 m/s](https://tex.z-dn.net/?f=v%20%3D%206.4%20%5Ctimes%2010%5E3%20m%2Fs)
Part b)
Now proton is revolving in the field of outer cylinder only
so again we have
![qvB_1 = \frac{mv^2}{R}](https://tex.z-dn.net/?f=qvB_1%20%3D%20%5Cfrac%7Bmv%5E2%7D%7BR%7D)
![(1.6 \times 10^{-19})(15)\times 10^{-3} = \frac{1.66\times 10^{-27} v}{16.9 \times 10^{-3}}](https://tex.z-dn.net/?f=%281.6%20%5Ctimes%2010%5E%7B-19%7D%29%2815%29%5Ctimes%2010%5E%7B-3%7D%20%3D%20%5Cfrac%7B1.66%5Ctimes%2010%5E%7B-27%7D%20v%7D%7B16.9%20%5Ctimes%2010%5E%7B-3%7D%7D)
![v = 2.44 \times 10^4 m/s](https://tex.z-dn.net/?f=v%20%3D%202.44%20%5Ctimes%2010%5E4%20m%2Fs)
Answer:
<em>The rock reaches a maximum height of 442.225 m and was thrown at a speed of 93.1 m/s</em>
Explanation:
<u>Vertical Launch</u>
The rock is launched up with a certain speed vo, it reaches its highest point at a height h when the speed is zero, and then it stars a free-fall motion until it hits the ground at time t.
The maximum height is given by
![\displaystyle h=\frac{g\cdot t^2}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20h%3D%5Cfrac%7Bg%5Ccdot%20t%5E2%7D%7B2%7D)
The rock takes the same time to reach this point as to return to the ground, thus we can calculate the maximum height
![\displaystyle h=\frac{9.8\cdot 9.5^2}{2}=442.225\ m](https://tex.z-dn.net/?f=%5Cdisplaystyle%20h%3D%5Cfrac%7B9.8%5Ccdot%209.5%5E2%7D%7B2%7D%3D442.225%5C%20m)
The rock was thrown up at a speed
![v_o=gt=9.8\cdot 9.5=93.1 \ m/s](https://tex.z-dn.net/?f=v_o%3Dgt%3D9.8%5Ccdot%209.5%3D93.1%20%5C%20m%2Fs)