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
B
R3
C
R4
D
None of these

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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