Question

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

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

Answer 1

Answer: (C)

$7.5R$

Distance between the surface of the spherical bodies $=12R-R-2R=9R$
Force $\propto$ Mass
Acceleration $\propto$ Mass
Distance $\propto$ Acceleration
$\Rightarrow \frac{a_1}{a_2}=\frac{M}{5M}=\frac{1}{5}\Rightarrow \frac{S_1}{S_2}=\frac{1}{5}\Rightarrow S_2=5S_1$
$S_1+S_2=9$
$\Rightarrow 6S_1=9\Rightarrow S_1=\frac{9}{6}=1.5$
$S_2=1.5\times 5=7.5$
Note: Maximum distance will be travelled by smaller bodies due to the greater acceleration caused by the same gravitational force