what happens to the force of attraction between two planets if their masses are doubled and the distance…
what happens to the force of attraction between two planets if their masses are doubled and the distance between them is also doubled?\nview available hint(s)\nhint 1.\nwhat is the gravitational force proportional to?\nthe force would double.\nthe force would remain the same.\nthe force would quadruple.\nit would be half of the original force.
Answer
Explanation:
Step1: Recall gravitational - force formula
The gravitational - force formula is $F = G\frac{m_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them.
Step2: Calculate the new force
Let the original masses be $m_1$ and $m_2$, and the original distance be $r$. The original force is $F_1=G\frac{m_1m_2}{r^2}$. After the masses are doubled ($m_1' = 2m_1$, $m_2' = 2m_2$) and the distance is doubled ($r' = 2r$), the new force $F_2$ is $F_2=G\frac{(2m_1)(2m_2)}{(2r)^2}$.
Step3: Simplify the new - force expression
$F_2=G\frac{4m_1m_2}{4r^2}=G\frac{m_1m_2}{r^2}$.
Answer:
The force would remain the same.