UnkleRhaukus
  • UnkleRhaukus
A neutron star has a mass about \(1.5\) times that of the sun; its radius is \(10 [\text{km}]\). A mass, m, falls onto the neutron star from a very large distance (\(1000 [\text{km}]\)). What is the approximate speed at which the mass reaches the surface of the neutron star? Relativistic effects should be ignored here. You might need to use some of the following constants: \[R_\odot=7.0\times10^8[\text m]\\ G=6.67\times10^{−11}[\text m^3/\text{kg}\cdot\text s^2] \\ M_\odot=1.9891\times10^{30}[\text{kg}]\] \[ •\quad1\times10^8 [\text {m}/\text s]\\ •\quad1.4\times10^8 [\text {m}/\text s]\\ •\quad2\times10^8 [\text {m}/\text s]\\ •\quad2.8\times10^8 [\text {m}/\text s]\\ •\quad4\times10^8 [\text {m}/\text s] \]
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
UnkleRhaukus
  • UnkleRhaukus
|dw:1370596496834:dw|
UnkleRhaukus
  • UnkleRhaukus
\[U_\text{max}=G\frac{mM}R\\KE_\text{max}=\tfrac12mv^2\] \[mv^2=G\frac{mM}R\\\quad v=\sqrt{\frac{2GM}R}\]
UnkleRhaukus
  • UnkleRhaukus
\[U_\text{max}=G\frac{mM}r\\KE_\text{max}=\tfrac12mv^2\] \[mv^2=G\frac{mM}r\\\quad v=\sqrt{\frac{2GM}r}\]

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UnkleRhaukus
  • UnkleRhaukus
\[v=\sqrt{\frac{2\times6.67\times10^{-11}\left[\text {m}^3/\text{kg}\cdot\text s^2\right]\times1.5\times1.9891\times10^{30}[\text{kg}]}{1000[\text {km}]}}\\ \quad=\sqrt{2\times6.67\times1.5\times1.9891\times10^{-11+30-6}\left[\text {m}^2\cdot\text s^2\right]}\\\quad\approx\sqrt{39.8\times10^{13}}\left[\text {m}/\text s\right]\\\quad\approx2\times10^7\left[\text {m}/\text s\right]\]
UnkleRhaukus
  • UnkleRhaukus
My result isn't close enough to any of the options, where am i going wrong?
UnkleRhaukus
  • UnkleRhaukus
*typo\[\tfrac12mv^2=G\frac{mM}R\]
IrishBoy123
  • IrishBoy123
see attached, the full answer is 198504085.83 or 2x10^8
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