Answer:
36 N
Explanation:
If the object of mass, m = 8 kg is swung in a horizontal circle of radius, r = 2m = length of string with tangential velocity v = 3 m/s, the tension in the string is the centripetal force which is T = mv²/r
= 8 kg × (3 m/s)²/2 m
= 4 kg × 9 m/s²
= 36 N
Given :
An electron moving in the positive x direction experiences a magnetic force in the positive z direction.
To Find :
The direction of the magnetic field.
Solution :
We know, force is given by :
![\vec{F}=q(\vec{v}\times \vec{B)}](https://tex.z-dn.net/?f=%5Cvec%7BF%7D%3Dq%28%5Cvec%7Bv%7D%5Ctimes%20%5Cvec%7BB%29%7D)
Here, q = -e.
![\vec{F}=(-e)(\vec{v}\times \vec{B)}\\\\\hat{k}=(-e)(\hat{i}\times \vec{B})](https://tex.z-dn.net/?f=%5Cvec%7BF%7D%3D%28-e%29%28%5Cvec%7Bv%7D%5Ctimes%20%5Cvec%7BB%29%7D%5C%5C%5C%5C%5Chat%7Bk%7D%3D%28-e%29%28%5Chat%7Bi%7D%5Ctimes%20%5Cvec%7BB%7D%29)
Now, for above condition to satisfy :
![\hat{i}\times \vec{B}=-\hat{k}](https://tex.z-dn.net/?f=%5Chat%7Bi%7D%5Ctimes%20%5Cvec%7BB%7D%3D-%5Chat%7Bk%7D)
So, ![\vec{B}=-\hat{j}](https://tex.z-dn.net/?f=%5Cvec%7BB%7D%3D-%5Chat%7Bj%7D)
Therefore, direction of magnetic field is negative y direction.
Hence, this is the required solution.
Explanation:
Given that,
(a) Speed, ![v=6.66\times 10^6\ m/s](https://tex.z-dn.net/?f=v%3D6.66%5Ctimes%2010%5E6%5C%20m%2Fs)
Mass of the electron, ![m_e=9.11\times 10^{-31}\ kg](https://tex.z-dn.net/?f=m_e%3D9.11%5Ctimes%2010%5E%7B-31%7D%5C%20kg)
Mass of the proton, ![m_p=1.67\times 10^{-27}\ kg](https://tex.z-dn.net/?f=m_p%3D1.67%5Ctimes%2010%5E%7B-27%7D%5C%20kg)
The wavelength of the electron is given by :
![\lambda_e=\dfrac{h}{m_ev}](https://tex.z-dn.net/?f=%5Clambda_e%3D%5Cdfrac%7Bh%7D%7Bm_ev%7D)
![\lambda_e=\dfrac{6.63\times 10^{-34}}{9.11\times 10^{-31}\times 6.66\times 10^6}](https://tex.z-dn.net/?f=%5Clambda_e%3D%5Cdfrac%7B6.63%5Ctimes%2010%5E%7B-34%7D%7D%7B9.11%5Ctimes%2010%5E%7B-31%7D%5Ctimes%206.66%5Ctimes%2010%5E6%7D)
![\lambda_e=1.09\times 10^{-10}\ m](https://tex.z-dn.net/?f=%5Clambda_e%3D1.09%5Ctimes%2010%5E%7B-10%7D%5C%20m)
The wavelength of the proton is given by :
![\lambda_p=\dfrac{h}{m_p v}](https://tex.z-dn.net/?f=%5Clambda_p%3D%5Cdfrac%7Bh%7D%7Bm_p%20v%7D)
![\lambda_p=\dfrac{6.63\times 10^{-34}}{1.67\times 10^{-27}\times 6.66\times 10^6}](https://tex.z-dn.net/?f=%5Clambda_p%3D%5Cdfrac%7B6.63%5Ctimes%2010%5E%7B-34%7D%7D%7B1.67%5Ctimes%2010%5E%7B-27%7D%5Ctimes%206.66%5Ctimes%2010%5E6%7D)
![\lambda_p=5.96\times 10^{-14}\ m](https://tex.z-dn.net/?f=%5Clambda_p%3D5.96%5Ctimes%2010%5E%7B-14%7D%5C%20m)
(b) Kinetic energy, ![K=1.71\times 10^{-15}\ J](https://tex.z-dn.net/?f=K%3D1.71%5Ctimes%2010%5E%7B-15%7D%5C%20J)
The relation between the kinetic energy and the wavelength is given by :
![\lambda_e=\dfrac{h}{\sqrt{2m_eK}}](https://tex.z-dn.net/?f=%5Clambda_e%3D%5Cdfrac%7Bh%7D%7B%5Csqrt%7B2m_eK%7D%7D)
![\lambda_e=\dfrac{6.63\times 10^{-34}}{\sqrt{2\times 9.11\times 10^{-31}\times 1.71\times 10^{-15}}}](https://tex.z-dn.net/?f=%5Clambda_e%3D%5Cdfrac%7B6.63%5Ctimes%2010%5E%7B-34%7D%7D%7B%5Csqrt%7B2%5Ctimes%209.11%5Ctimes%2010%5E%7B-31%7D%5Ctimes%201.71%5Ctimes%2010%5E%7B-15%7D%7D%7D)
![\lambda_e=1.18\times 10^{-11}\ m](https://tex.z-dn.net/?f=%5Clambda_e%3D1.18%5Ctimes%2010%5E%7B-11%7D%5C%20m)
![\lambda_p=\dfrac{h}{\sqrt{2m_pK}}](https://tex.z-dn.net/?f=%5Clambda_p%3D%5Cdfrac%7Bh%7D%7B%5Csqrt%7B2m_pK%7D%7D)
![\lambda_p=\dfrac{6.63\times 10^{-34}}{\sqrt{2\times 1.67\times 10^{-27}\times 1.71\times 10^{-15}}}](https://tex.z-dn.net/?f=%5Clambda_p%3D%5Cdfrac%7B6.63%5Ctimes%2010%5E%7B-34%7D%7D%7B%5Csqrt%7B2%5Ctimes%201.67%5Ctimes%2010%5E%7B-27%7D%5Ctimes%201.71%5Ctimes%2010%5E%7B-15%7D%7D%7D)
![\lambda_p=2.77\times 10^{-13}\ m](https://tex.z-dn.net/?f=%5Clambda_p%3D2.77%5Ctimes%2010%5E%7B-13%7D%5C%20m)
Hence, this is the required solution.
Answer:
i would say a) two playlists
hope this helps!
Explanation: