Question

Part A Is there change in the torce of gravity between two objects when their masses are doubied and the distance behwaen them is also doubled? The force of gravity is doubled The force of gravity is tripled O The force of gravity is quadrupled There is no change. Submi Request Answer Provide Feedback

Answer 1

$\text{Solution :}\\ \text{The gravitational force between two objects } m_1\ \text{and} \ m_2 \text{ is as follows :}\\ F= \dfrac{G\ m_1 \ m_2}{r^2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text(i) \\ {\boldsymbol {Now} ; }\\ \text{Masses of the objects are doubled and the distance b/w them is also doubled. }\\ m_1^{new} =2m_1, \ \ \ \ \ \ \ \ \ \ \ m_2^{new}=2m_2 , \ \ \ \ \ \ \ \ \ \ \ r_{new}= 2r \\ \text{Gravitational Force in new case ;}\\ F_{new} =\dfrac{G \ m_1^{new}\ m_2^{new}}{r_{new}^2}\\ F_{new} =\dfrac{G \ (2\times m_1)\times (2\times m_2)}{(2\times r)^2}\\ F_{new}= \dfrac{G\ m_1 \ m_2}{r^2}\\ F_{new}= F \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{From equation} (i) ]\\ \text{Answer: There is no change.}$