MCQ
Two identical solid copper spheres of radius $R$ placed in contact with each other. The gravitational attracton between them is proportional to
- A$R^2$
- B$R^{-2}$
- ✓$R^4$
- D$R^{-4}$
✓
Answer
Correct option: C.
$R^4$
c
(c) $F = \frac{{G \times m \times m}}{{{{(2R)}^2}}}$=$\frac{{G \times {{\left( {\frac{4}{3}\pi {R^3}\rho } \right)}^2}}}{{4{R^2}}}$$ = \frac{4}{9}{\pi ^2}{\rho ^2}{R^4}$
(c) $F = \frac{{G \times m \times m}}{{{{(2R)}^2}}}$=$\frac{{G \times {{\left( {\frac{4}{3}\pi {R^3}\rho } \right)}^2}}}{{4{R^2}}}$$ = \frac{4}{9}{\pi ^2}{\rho ^2}{R^4}$
$F \propto {R^4}$
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