Question

10. When the distance between two bodies is doubled and mass of each body is also doubled then the
gravitational force will be
a) doubled
b) Remained constant c) Trebled
d) Quadrupled​

Answer 1

GiveN :-

• The distance between two bodies is doubled and mass of each body is also doubled .

To FinD :-

• The change in gravitational force.

SolutioN :-

Given that the distance between two bodies is doubled and mass of each body is also doubled . We need to find the change in the Gravitational Force . We know gravitational force as G m1 m2/r². Where ,

$\red{\frak{Where}}\begin{cases}\textsf{ Mass of first body is \textbf{m} _1 . }\\\textsf{ Mass of the second body is \textbf{m} _2 . } \\\textsf{ The distance of seperation is \textbf{r} .}\end{cases}$

$\underline\red{\textbf {When the Distance and mass is doubled:-}}$

$\sf:\implies \pink{ Force_{(gravitational)}= G\dfrac{m_1m_2}{r^2}}\\\\\sf:\implies F_2 = G\dfrac{(2m_1)(2m_2)}{(2r)^2} \\\\\sf:\implies F_2=G \dfrac{4m_1m_2}{4r^2} \\\\\sf:\implies \boxed{\frak{\pink{ F_2=G \dfrac{m_1m_2}{r^2} }}}$

Hence we see that the Force remains constant as of first situation . Hence the force remains same .