NEET-XII-Physics
11: Gravitation
- #14A uniform metal sphere of radius a and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4a (figure 11-E2). The centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points P1 and P2 shown in the figure
Figure
Ans : At point P1, the gravitational field due to the sphere and the shell is given by
F`` =\frac{GM}{{\left(3a+a\right)}^{2}}+0=\frac{GM}{16{a}^{2}}``
At point P2, the gravitational field due to the sphere and the shell is given by
`` F=\frac{\,\mathrm{\,GM\,}}{{\left(a+4a+a\right)}^{2}}+\frac{\,\mathrm{\,GM\,}}{{\left(4a+a\right)}^{2}}``
`` \Rightarrow F=\frac{\,\mathrm{\,GM\,}}{36{a}^{2}}+\frac{\,\mathrm{\,GM\,}}{25{a}^{2}}``
`` \Rightarrow F=\frac{\,\mathrm{\,GM\,}}{{a}^{2}}\left(\frac{1}{36}+\frac{1}{25}\right)``
`` \Rightarrow F=\frac{\,\mathrm{\,GM\,}}{{a}^{2}}\left(\frac{25+36}{900}\right)``
`` \Rightarrow F=\left(\frac{61}{900}\right)\frac{\,\mathrm{\,GM\,}}{{a}^{2}}``
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