Distance Covered Before Collision – Rankers Physics
Topic: Center of Mass , Momentum and Collision
Subtopic: Calculation of Center of Mass

Distance Covered Before Collision

Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$ 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 before collision is :

(2015)

$4.5R$
$7.5R$
$1.5R$
$2.5R$

Solution:

The centre of mass remains stationary. Initial distance of COM from mass $M$ is $\frac{5M \times 12R}{M + 5M} = 10R$. At collision, distance between centers is $3R$, and the distance of $M$ from COM is $\frac{5}{6} \times 3R = 2.5R$. Thus, distance covered by $M$ is $10R - 2.5R = 7.5R$. Option (b) is correct.

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