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  4. 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 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is :

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Q. 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 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is :

AIPMTAIPMT 2015

Solution:

At time of collision the distance between their centers = 3R So total distance travelled by both=12R - 3R = 9R FOR MORE. Since the bodies move under mutual forces, center of mass will remain stationary so
$\ce{m_1x_1 = m_2x_2}$
$\ce{mx = 5m(9R -x )}$
$\ce{x = 45R - 5x}$
$\ce{6x = 45R}$
$\ce{x = \frac{45}{6}R}$

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