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Gravitation — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsGravitation2 Marks
Question
A uniform metal sphere of radius a and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4a The centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points $P_1$ and $P_2$ shown in the figure.
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Answer

At $P_1$, Gravitational field due to sphere $\text{M}=\frac{\text{GM}}{(3\text{a}+\text{a})^2}=\frac{\text{GM}}{16\text{a}^2}$ At $P_2$, Gravitational field is due to sphere & shell,$=\frac{\text{GM}}{(\text{a}+4\text{a}+\text{a})^2}+\frac{\text{GM}}{(\text{4a}+\text{a})^2}$
$=\frac{\text{GM}}{\text{a}^2}\Big(\frac{1}{36}+\frac{1}{25}\Big)=\Big(\frac{61}{900}\Big)\frac{\text{GM}}{\text{a}^2}$

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