D, it provides greater accuracy for measuring stars far from the earth.
Answer:
the radius of the protons path is r = 0.85 m.
Explanation:
the force due to magnetic fields lead to the cetripetal force, such that:
F = q×v×B = m×(v^2)/r
q×B = m×v/r
then:
r = m×v/q×B
r = p/q×B
then, the kinetic energy of the proton:
K = 1/2×m×v^2 = p^2/(2×m)
q×B = \sqrt{2×m×K}/r
r = \sqrt{2×m×K}/(q×B)
= \sqrt{2×(1.67×10^-27)×(5.3×1.60×10^-13)}/(1.60×10^-19×0.39)
= 0.85 m
Answer:
![\boxed{\sf Acceleration \ (a) = 2 \ m/s^{2}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%5Csf%20Acceleration%20%5C%20%28a%29%20%3D%202%20%5C%20m%2Fs%5E%7B2%7D%7D%20)
![\boxed{\sf Distance \ covered \ (s) = 100 \ m}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%5Csf%20Distance%20%5C%20covered%20%5C%20%28s%29%20%3D%20100%20%5C%20m%7D%20)
Given:
Initial velocity (u) = 0 m/s
Final velocity (v) = 20 m/s
Time taken (t) = 10 sec
To Find:
(i) Acceleration (a)
(ii) Distance covered (s)
Explanation:
![\sf (i) \ From \ 1^{st} \ equation \ of \ motion:](https://tex.z-dn.net/?f=%5Csf%20%28i%29%20%5C%20From%20%5C%201%5E%7Bst%7D%20%5C%20equation%20%5C%20of%20%5C%20motion%3A)
![\sf \implies v = u + at](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20v%20%3D%20u%20%2B%20at)
![\sf \implies 20 = 0 + a(10)](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%2020%20%3D%200%20%2B%20a%2810%29)
![\sf \implies 10a = 20](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%2010a%20%3D%2020)
![\sf \implies \frac{10a}{10} = \frac{20}{10}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20%5Cfrac%7B10a%7D%7B10%7D%20%20%3D%20%20%5Cfrac%7B20%7D%7B10%7D%20)
![\sf \implies a = 2 \: m/ {s}^{2}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20a%20%3D%202%20%5C%3A%20m%2F%20%7Bs%7D%5E%7B2%7D%20)
![\sf (ii) \ From \ 2^{nd} \ equation \ of \ motion:](https://tex.z-dn.net/?f=%5Csf%20%28ii%29%20%5C%20From%20%5C%202%5E%7Bnd%7D%20%5C%20equation%20%5C%20of%20%5C%20motion%3A)
![\sf \implies s = ut + \frac{1}{2} a {t}^{2}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20s%20%3D%20ut%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20a%20%7Bt%7D%5E%7B2%7D%20)
![\sf \implies s = (0)(10) + \frac{1}{2} \times 2 \times {(10)}^{2}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20s%20%3D%20%280%29%2810%29%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%202%20%5Ctimes%20%20%7B%2810%29%7D%5E%7B2%7D%20)
![\sf \implies s = \frac{1}{ \cancel{2}} \times \cancel{2} \times {(10)}^{2}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20s%20%3D%20%20%5Cfrac%7B1%7D%7B%20%5Ccancel%7B2%7D%7D%20%20%5Ctimes%20%20%5Ccancel%7B2%7D%20%5Ctimes%20%20%7B%2810%29%7D%5E%7B2%7D%20)
![\sf \implies s = {10}^{2}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20s%20%3D%20%20%7B10%7D%5E%7B2%7D%20)
![\sf \implies s = 100 \: m](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20s%20%3D%20100%20%5C%3A%20m)