Question

Two spherical bodies of mass m and 5m, radius R and 2R respectively are released in free space with an initial separation of 12 R between their centres. If they attract each other due to gravitational force alone, then the distance covered by the smaller body just before the collision is

• A. 2.5 R
• B. 4.5 R
• C. 7.5 R
• D. 1.5 R

Answer 1

The correct option is C 7.5 R


$F=\frac{Gm\left(5m\right)}{(12R-x{)}^2}$
$\therefore a_{small}=\frac{F}{m}=\frac{G\left(5m\right)}{(12R-x{)}^2}$
$a_{big}=\frac{F}{5m}=\frac{Gm}{(12R-x{)}^2}$
$\therefore x=\frac{1}{2}{a}_{small}{t}^2=\frac{1}{2}\frac{G5m}{(12R-x{)}^2}{t}_2^2\dots \left(1\right)$
$9R-x=\frac{1}{2}{a}_{big}{t}^2=\frac{1}{2}\frac{G\left(m\right)}{(12R-x{)}^2}{t}^2\dots \left(2\right)$
$\left(1\right)÷\left(2\right)\Rightarrow x=7.5R$