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NEET 2015
Exam
NEET
Year
2015
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

NEET 2015 · Physics · Center of Mass, Momentum and Collision

Two spherical bodies of mass M and 5M and radii R and 2R released...

Two spherical bodies of mass M and 5M and radii R and 2R 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:Two spherical bodies of mass M and 5M and radii R and 2R released in free space with initial separation between their

Options

  1. A2.5R
  2. B4.5R
  3. C7.5R
  4. D1.5R

Correct answer

C. 7.5R

Step-by-step solution

Initial position,
Two spherical bodies of mass M and 5M and radii R and 2R released in free space with initial separation between their
For collision, both bodies have to travel distance =12R−3R=9R= 12R - 3R = 9R

Since the bodies move under the mutual forces, centre of mass will remains stationary,
m1x1=m2x2{m}_{1}{x}_{1} = {m}_{2}{x}_{2}
Mx=5M(9R−x)Mx = 5M ( 9R - x )
x=45R−5xx = 45R - 5x
6x=45R6x = 45R
x=45RR=7.5Rx = \dfrac{45}{R}R = 7.5R
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