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Center of Mass as an Average Point

Find the grav...

Question

Find the gravitational field intensity at point $P_{2}$

A

\frac{21 G M}{{900 a}^{2}}

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B

\frac{61 G M}{{450 a}^{2}}

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C

\frac{61 G M}{{900 a}^{2}}

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D

\frac{61 G M}{{1800 a}^{2}}

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Solution

The correct option is A $\frac{61 G M}{{900 a}^{2}}$
Gravitational field intensity at $P_{2}$ due to shell= $\frac{G M}{(5 a)^{2}}$
Gravitational field intensity at $P_{2}$ due to sphere= $\frac{G M}{(6 a)^{2}}$
Therefore total gravitational field intensity at $P_{2} = \frac{61 G M}{900 a^{2}}$

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