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Question

Two identical spheres are placed in contact with each other. The force of gravitation between the spheres will be proportional to (R = radius of each sphere )


A
R
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B
R3
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C
R4
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D
None of these
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Solution

The correct option is B $$ R^4 $$

Gravitation force between them, $$F=\dfrac{G{{m}_{1}}{{m}_{2}}}{{{R}^{2}}}$$

$$F=\dfrac{G\left( \dfrac{4}{3}\pi {{R}^{3}} \right)\rho \left( \dfrac{4}{3}\pi {{R}^{3}} \right)\rho }{{{R}^{2}}}$$

$$F\propto {{R}^{4}}$$

Hence, force is directly proportional to $${{R}^{4}}$$ 


Physics

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