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. 1.5R
• B. 2.5R
• C. 4.5R
• D. 7.5R

Answer 1

The correct option is D 7.5R

Distance between their surfaces $=12R-R-2R=9R$

Since,

P $\propto$ mass

a $\propto$ mass

Distance $\propto$ acceleration

So, we can write;

$\frac{a_1}{a_2}=\frac{m}{5m}=\frac{s_1}{s_2}$

$\frac{s_1}{s_2}=\frac{1}{5}$

$5s_1=s_2$ .......................(1)

$s_1+s_2=9R$ .......................(2)

On solving these equations;

$s_1=1.5R$

$s_2=7.5R$

Since smaller ball have more acceleration in same time interval, smaller ball will cover more distance.