Consider two solid spheres of radii x\[{{R}_{1}}=1\text{ }m,\] |
\[{{R}_{2}}=2\text{ }m\] and masses \[{{M}_{1}}\]and \[{{M}_{2}},\]respectively. |
The gravitational field due to sphere and are shown. The value of\[\frac{{{M}_{1}}}{{{M}_{2}}}\] is |
[JEE MAIN Held On 08-01-2020 Morning] |
A)
\[\frac{1}{6}\] B)
\[\frac{1}{2}\]
C)
\[\frac{2}{3}\]
D)
\[\frac{1}{3}\]
Correct Answer:
A Solution :
Gravitation field at the surface \[E=\frac{Gm}{{{r}^{2}}}\] \[\therefore {{E}_{1}}=\frac{G{{m}_{1}}}{{{r}^{2}}_{1}}\] and \[{{E}_{2}}=\frac{G{{m}_{2}}}{{{r}^{2}}_{2}}\] \[\therefore \frac{{{E}_{1}}}{{{E}_{2}}}={{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)\] \[\therefore \frac{2}{3}={{\left( \frac{2}{1} \right)}^{2}}\left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)\] \[\Rightarrow \left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)=\frac{1}{6}\]
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